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ASTM E1876-07

(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

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 the standard.
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.

General Information

Status
Historical
Publication Date
31-May-2007
ICS
81.060.20 - Ceramic products
Technical Committee
E28 - Mechanical Testing
Drafting Committee
E28.04 - Uniaxial Testing
Current Stage
Ref Project

Relations

Replaces
ASTM E1876-01(2006) - Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Impulse Excitation of Vibration
Effective Date
01-Jun-2007
Replaced By
ASTM E1876-09 - Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Impulse Excitation of Vibration
Effective Date
01-Apr-2009
Referred By
ASTM B925-15(2022) - Standard Practices for Production and Preparation of Powder Metallurgy (PM) Test Specimens
Effective Date
01-Jun-2007
Referred By
ASTM C1259-21 - Standard Test Method for Dynamic Young’s Modulus, Shear Modulus, and Poisson’s Ratio for Advanced Ceramics by Impulse Excitation of Vibration
Effective Date
01-Jun-2007
Referred By
ASTM E2001-18 - Standard Guide for Resonant Ultrasound Spectroscopy for Defect Detection in Both Metallic and Non-metallic Parts
Effective Date
01-Jun-2007
Referred By
ASTM E2546-15(2023) - Standard Practice for Instrumented Indentation Testing
Effective Date
01-Jun-2007
Referred By
ASTM E1875-20a - Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Sonic Resonance
Effective Date
01-Jun-2007
Referred By
ASTM F2516-22 - Standard Test Method for Tension Testing of Nickel-Titanium Superelastic Materials
Effective Date
01-Jun-2007
Referred By
ASTM C1198-20 - Standard Test Method for Dynamic Young’s Modulus, Shear Modulus, and Poisson’s Ratio for Advanced Ceramics by Sonic Resonance
Effective Date
01-Jun-2007
Referred By
ASTM F3122-14(2022) - Standard Guide for Evaluating Mechanical Properties of Metal Materials Made via Additive Manufacturing Processes
Effective Date
01-Jun-2007

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ASTM E1876-07 - Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Impulse Excitation of VibrationASTM E1876-07 - Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Impulse Excitation of Vibration
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ASTM E1876-07 - Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Impulse Excitation of Vibration
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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: E 1876 – 07
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 (e) indicates an editorial change since the last revision or reapproval.
1. Scope 1.5 This standard does not purport to address all of the
safety concerns, if any, associated with its use. It is the
1.1 This test method covers determination of the dynamic
responsibility of the user of this standard to establish appro-
elastic properties of elastic materials at ambient temperatures.
priate safety and health practices and determine the applica-
Specimens of these materials possess specific mechanical
bility of regulatory limitations prior to use.
resonant frequencies that are determined by the elastic modu-
lus, mass, and geometry of the test specimen. The dynamic
2. Referenced Documents
elasticpropertiesofa material can therefore be computedifthe
2
2.1 ASTM Standards:
geometry, mass, and mechanical resonant frequencies of a
C 215 Test Method for Fundamental Transverse, Longitu-
suitable (rectangular or cylindrical geometry) test specimen of
dinal, and Torsional Resonant Frequencies of Concrete
that material can be measured. Dynamic Young’s modulus is
Specimens
determined using the resonant frequency in either the flexural
C 372 Test Method for Linear Thermal Expansion of Por-
orlongitudinalmodeofvibration.Thedynamicshearmodulus,
celain Enamel and Glaze Frits and Fired Ceramic Whitew-
or modulus of rigidity, is found using torsional resonant
are Products by the Dilatometer Method
vibrations. Dynamic Young’s modulus and dynamic shear
C 623 Test Method for Young’s Modulus, Shear Modulus,
modulus are used to compute Poisson’s ratio.
and Poisson’s Ratio for Glass and Glass-Ceramics by
1.2 Although not specifically described herein, this test
Resonance
method can also be performed at cryogenic and high tempera-
C 747 Test Method for Moduli of Elasticity and Fundamen-
tures with suitable equipment modifications and appropriate
tal Frequencies of Carbon and Graphite Materials by Sonic
modifications to the calculations to compensate for thermal
Resonance
expansion.
C 848 Test Method for Young’s Modulus, Shear Modulus,
1.3 There are material specific ASTM standards that cover
and Poisson’s Ratio For Ceramic Whitewares by Reso-
the determination of resonance frequencies and elastic proper-
nance
ties of specific materials by sonic resonance or by impulse
C 1161 Test Method for Flexural Strength of Advanced
excitation of vibration. Test Methods C 215, C 623, C 747,
Ceramics at Ambient Temperature
C 848, C 1198, and C 1259 may differ from this test method in
C 1198 Test Method for Dynamic Young’s Modulus, Shear
several areas (for example; sample size, dimensional toler-
Modulus, and Poisson’s Ratio for Advanced Ceramics by
ances, sample preparation). The testing of these materials shall
Sonic Resonance
be done in compliance with these material specific standards.
C 1259 Test Method for Dynamic Young’s Modulus, Shear
Where possible, the procedures, sample specifications and
Modulus, and Poisson’s Ratio for Advanced Ceramics by
calculations are consistent with these test methods.
Impulse Excitation of Vibration
1.4 The values stated in SI units are to be regarded as the
E6 Terminology Relating to Methods of Mechanical Test-
standard.
ing
1
This test method is under the jurisdiction of ASTM Committee E28 on
2
Mechanical Testing and is the direct responsibility of Subcommittee E28.04 on For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Uniaxial Testing. contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Current edition approved June 1, 2007. Published June 2007. Originally Standards volume information, refer to the standard’s Document Summary page on
approved in 1997. Last previous edition approved in 2006 as E 1876 – 01(2006). the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
1

---------------------- Page: 1 ----------------------
E1876–07
E 177 Practice for Use of the Terms Precision and Bias in 3.2.5 in-plane flexure, n—for rectangular parallelepiped
ASTM Test Methods geometries, a flexure mode in which the direction of displace-
ment is in the major plane of the test specimen.
3. Terminology
3.2.6 isotropic, adj—the condition of a specimen such that
thevaluesoftheelasticpropertiesarethesameinalldirections
3.1 Definitions—The definitions of terms relating to me-
in the material. Materials are considered isotropic o
...

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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.  
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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...
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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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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.
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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  
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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.  
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1.1 This terminology pertains to the terminology used in ceramic whitewares and related products.  
1.2 Words adequately defined in standard dictionaries are not included. Included are words that are peculiar to this industry. Double words, hyphenated words, or phrases are listed alphabetically under the first word; additional important words are cross-referenced.  
1.3 For definitions of terms relating to surface imperfections on ceramics, refer to Terminology F109.  
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Standard Practice for Fractographic Analysis of Fracture Mirror Sizes in Ceramics and Glasses

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5.1 Fracture mirror size analysis is a powerful tool for analyzing glass and ceramic fractures. Fracture mirrors are tell-tale fractographic markings in brittle materials that surround a fracture origin as discussed in Practices C1256 and C1322. Fig. 1 shows a schematic with key features identified. Fig. 2 shows an example in glass. The fracture mirror region is very smooth and highly reflective in glasses, hence the name “fracture mirror.” In fact, high magnification microscopy reveals that, even within the mirror region in glasses, there are very fine features and escalating roughness as the crack advances away from the origin. These are submicrometer in size and hence are not discernable with an optical microscope. Early investigators interpreted fracture mirrors as having discrete boundaries including a “mirror-mist” boundary and also a “mist-hackle” boundary in glasses. These were also termed “inner mirror” or “outer mirror” boundaries, respectively. It is now known that there are no discrete boundaries corresponding to specific changes in the fractographic features. Surface roughness increases gradually from well within the fracture mirror to beyond the apparent boundaries. The boundaries were a matter of interpretation, the resolving power of the microscope, and the mode of viewing. In very weak specimens, the mirror may be larger than the specimen or component and the boundaries will not be present. Eq 1 is hereafter referred to as the “empirical stress – fracture mirror size relationship,” or “stress-mirror size relationship” for short. A review of the history of Eq 1, and fracture mirror analysis in general, may be found in Refs (1)3 and (2).  
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1.1 This practice pertains to the analysis and interpretation of fracture mirror sizes in brittle materials. Fracture mirrors (Fig. 1) are telltale fractographic markings that surround a fracture origin in brittle materials. The fracture mirror size may be used with known fracture mirror constants to estimate the stress in a fractured component. Alternatively, the fracture mirror size may be used in conjunction with known stresses in test specimens to calculate fracture mirror constants. The practice is applicable to glasses and polycrystalline ceramic laboratory test specimens as well as fractured components. The analysis and interpretation procedures for glasses and ceramics are similar, but they are not identical. Different optical microscopy examination techniques are listed and described, including observation angles, illumination methods, appropriate magnification, and measurement protocols. Guidance is given for calculating a fracture mirror constant and for interpreting the fracture mirror size and shape for both circular and noncircular mirrors including stress gradients, geometrical effects, residual stresses, or combinations thereof. The practice provides figures and micrographs illustrating the different types of features commonly observed in and measurement techniques used for the fracture mirrors of glasses and polycrystalline ceramics.
FIG. 1 Schematic of a Fracture Mirror Centered on a Surface Flaw of Initial Size (a)
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Standard Terminology Relating to Surface Imperfections on Ceramics

SCOPE
1.1 This terminology describes and illustrates imperfections observed on whitewares and related products. For additional definitions of terms relating to whitewares and related products, refer to Terminology C242. To observe these defects, examination shall be performed visually, with or without the aid of a dye penetrant, as described in Test Method C949. Agreement by the manufacturer and the purchaser regarding specific techniques of observation is strongly recommended.  
1.2 This terminology does not cover every defect or imperfection possible for whitewares or related products. The standard is not intended to be an all inclusive document for ceramic imperfections. New defect types may be created as ceramic processes, materials, and technology evolve.  
1.3 Some of the imperfection photos utilize magnification for clarity in documentation. Unless otherwise noted, typical observation conditions for detection of tile imperfections/defects shall consist of current ANSI A137.1 viewing criteria for the specific defect type  
1.4 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.

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  • Standard
    64 pages
    English language
    sale 15% off