ASTM C623-21

Standard Test Method for Young's Modulus, Shear Modulus, and Poisson's Ratio for Glass and Glass-Ceramics by Resonance

SIGNIFICANCE AND USE
4.1 This test system has advantages in certain respects over the use of static loading systems in the measurement of glass and glass-ceramics:  
4.1.1 Only minute stresses are applied to the specimen, thus minimizing the possibility of fracture.  
4.1.2 The period of time during which stress is applied and removed is of the order of hundreds of microseconds, making it feasible to perform measurements at temperatures where delayed elastic and creep effects proceed on a much-shortened time scale, as in the transformation range of glass, for instance.  
4.2 The test is suitable for detecting whether a material meets specifications, if cognizance is given to one important fact: glass and glass-ceramic materials are sensitive to thermal history. Therefore the thermal history of a test specimen must be known before the moduli can be considered in terms of specified values. Material specifications should include a specific thermal treatment for all test specimens.
SCOPE
1.1 This test method covers the determination of the elastic properties of glass and glass-ceramic materials. Specimens of these materials possess specific mechanical resonance frequencies which are defined by the elastic moduli, density, and geometry of the test specimen. Therefore the elastic properties of a material can be computed if the geometry, density, and mechanical resonance frequencies of a suitable test specimen of that material can be measured. Young's modulus is determined using the resonance frequency in the flexural mode of vibration. The shear modulus, or modulus of rigidity, is found using torsional resonance vibrations. Young's modulus and shear modulus are used to compute Poisson's ratio, the factor of lateral contraction.  
1.2 All glass and glass-ceramic materials that are elastic, homogeneous, and isotropic may be tested by this test method.2 The test method is not satisfactory for specimens that have cracks or voids that represent inhomogeneities in the material; neither is it satisfactory when these materials cannot be prepared in a suitable geometry. Non-glass and glass-ceramic materials should reference Test Method E1875 for non-material specific methodology to determine resonance frequencies and elastic properties by sonic resonance.
Note 1: Elastic here means that an application of stress within the elastic limit of that material making up the body being stressed will cause an instantaneous and uniform deformation, which will cease upon removal of the stress, with the body returning instantly to its original size and shape without an energy loss. Glass and glass-ceramic materials conform to this definition well enough that this test is meaningful.
Note 2: Isotropic means that the elastic properties are the same in all directions in the material. Glass is isotropic and glass-ceramics are usually so on a macroscopic scale, because of random distribution and orientation of crystallites.  
1.3 A cryogenic cabinet and high-temperature furnace are described for measuring the elastic moduli as a function of temperature from –195 to 1200 °C.  
1.4 Modification of the test for use in quality control is possible. A range of acceptable resonance frequencies is determined for a piece with a particular geometry and density. Any specimen with a frequency response falling outside this frequency range is rejected. The actual modulus of each piece need not be determined as long as the limits of the selected frequency range are known to include the resonance frequency that the piece must possess if its geometry and density are within specified tolerances.  
1.5 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
1.6 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, health, and environmental practices...

General Information

• Status: Published
• Publication Date: 31-May-2021
• ICS: 81.040.30 - Glass products
• ICS: 81.060.01 - Ceramics in general
• Technical Committee: C14 - Glass and Glass Products
• Drafting Committee: C14.04 - Physical and Mechanical Properties

Relations

• Refers: ASTM E1875-13 - Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Sonic Resonance
• Effective Date: 01-Nov-2013
• Refers: ASTM E1875-08 - Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Sonic Resonance
• Effective Date: 01-Dec-2008
• Refers: ASTM E1875-00 - Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Sonic Resonance
• Effective Date: 10-Oct-2000
• Refers: ASTM E1875-00e1 - Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Sonic Resonance
• Effective Date: 10-Oct-2000

Overview

ASTM C623-21 is the internationally recognized standard test method for determining the elastic properties of glass and glass-ceramic materials, specifically Young’s modulus, shear modulus, and Poisson’s ratio, using mechanical resonance techniques. Developed by ASTM International, this standard offers a non-destructive, highly sensitive approach to measure the elastic moduli of materials that are elastic, homogeneous, and isotropic, ensuring minimal risk of specimen fracture and allowing accurate analysis even at extreme temperatures ranging from –195°C to 1200°C.

Key Topics

• Measurement Advantages: Unlike static loading systems, the resonance method applies only minute stresses to the test specimen, which minimizes the chance of fracture. The rapid application and removal of stress (hundreds of microseconds) enables precise measurements, even at elevated temperatures where time-dependent deformation processes are significant.
• Property Determination: The technique involves detecting mechanical resonance frequencies of specimens with specific geometry and density. By measuring these frequencies, the modulus of elasticity (Young’s modulus), shear modulus (modulus of rigidity), and Poisson’s ratio can be calculated with high accuracy.
• Material Suitability: The method is applicable to glass and glass-ceramic materials that are elastic, homogeneous, and isotropic. Materials with cracks, voids, or unsuitable geometry are not recommended for this test.
• Thermal History Sensitivity: As the elastic properties of glass and glass-ceramics are influenced by their thermal history, it is crucial to account for any previous thermal treatments or processes when comparing measured moduli to specified values.
• Temperature-Dependent Testing: The standard accommodates testing at both cryogenic and high temperatures by describing the use of appropriate chambers and furnaces.

Applications

The ASTM C623-21 standard is essential in both research and quality control settings across a range of industries:

• Quality Control: This method can rapidly verify whether a glass or glass-ceramic batch meets mechanical specification limits, using resonance frequency ranges rather than full modulus calculations, thereby increasing testing efficiency.
• Product Development: By enabling precise measurement of elastic properties, the method supports material engineers in characterizing new glass and glass-ceramic formulations for targeted applications.
• Thermal Performance Assessment: The method’s capacity to assess moduli at varying temperatures is valuable for products expected to function in demanding thermal environments, such as aerospace or high-performance electronics.
• Specification Compliance: Many technical standards and procurement specifications require documented mechanical properties; this method provides a standardized, reproducible way to supply that data.

Related Standards

• ASTM E1875: "Test Method for Dynamic Young’s Modulus, Shear Modulus, and Poisson’s Ratio by Sonic Resonance" - Applicable to non-glass and more general materials, providing broader applicability for resonance testing methodologies.
• ISO and EN equivalents: While ASTM C623-21 is a key reference in North America, global industries may also reference similar international standards for mechanical testing of ceramics and glasses.

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Keywords: glass, glass-ceramic, Young’s modulus, shear modulus, Poisson’s ratio, resonance test method, ASTM C623-21, mechanical properties, quality control, elastic properties, materials testing, thermal history

Practical Value: ASTM C623-21 delivers robust, non-destructive evaluation of critical mechanical properties for glass and glass-ceramic materials, underpinning industry confidence in component quality, performance, and compliance.

Standards Content (Sample)

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: C623 − 21
Standard Test Method for
Young’s Modulus, Shear Modulus, and Poisson’s Ratio for
Glass and Glass-Ceramics by Resonance
This standard is issued under the fixed designation C623; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 1.3 A cryogenic cabinet and high-temperature furnace are
described for measuring the elastic moduli as a function of
1.1 This test method covers the determination of the elastic
temperature from–195 to 1200°C.
properties of glass and glass-ceramic materials. Specimens of
1.4 Modification of the test for use in quality control is
thesematerialspossessspecificmechanicalresonancefrequen-
possible. A range of acceptable resonance frequencies is
cies which are defined by the elastic moduli, density, and
determined for a piece with a particular geometry and density.
geometry of the test specimen. Therefore the elastic properties
Any specimen with a frequency response falling outside this
of a material can be computed if the geometry, density, and
frequency range is rejected. The actual modulus of each piece
mechanical resonance frequencies of a suitable test specimen
need not be determined as long as the limits of the selected
of that material can be measured. Young’s modulus is deter-
frequency range are known to include the resonance frequency
mined using the resonance frequency in the flexural mode of
that the piece must possess if its geometry and density are
vibration. The shear modulus, or modulus of rigidity, is found
within specified tolerances.
using torsional resonance vibrations. Young’s modulus and
shear modulus are used to compute Poisson’s ratio, the factor 1.5 The values stated in SI units are to be regarded as
of lateral contraction. standard. No other units of measurement are included in this
standard.
1.2 All glass and glass-ceramic materials that are elastic,
1.6 This standard does not purport to address all of the
homogeneous,andisotropicmaybetestedbythistestmethod.
safety concerns, if any, associated with its use. It is the
The test method is not satisfactory for specimens that have
responsibility of the user of this standard to establish appro-
cracks or voids that represent inhomogeneities in the material;
priate safety, health, and environmental practices and deter-
neither is it satisfactory when these materials cannot be
mine the applicability of regulatory limitations prior to use.
prepared in a suitable geometry. Non-glass and glass-ceramic
1.7 This international standard was developed in accor-
materials should reference Test Method E1875 for non-
dance with internationally recognized principles on standard-
materialspecificmethodologytodetermineresonancefrequen-
ization established in the Decision on Principles for the
cies and elastic properties by sonic resonance.
Development of International Standards, Guides and Recom-
NOTE 1—Elastic here means that an application of stress within the
mendations issued by the World Trade Organization Technical
elastic limit of that material making up the body being stressed will cause
Barriers to Trade (TBT) Committee.
aninstantaneousanduniformdeformation,whichwillceaseuponremoval
ofthestress,withthebodyreturninginstantlytoitsoriginalsizeandshape
2. Referenced Documents
without an energy loss. Glass and glass-ceramic materials conform to this
2.1 Reference to these documents shall be the latest issue
definition well enough that this test is meaningful.
unless otherwise specified by the authority applying this test
NOTE 2—Isotropic means that the elastic properties are the same in all
method.
directionsinthematerial.Glassisisotropicandglass-ceramicsareusually
so on a macroscopic scale, because of random distribution and orientation 3
2.2 ASTM Standards:
of crystallites.
E1875Test Method for Dynamic Young’s Modulus, Shear
Modulus, and Poisson’s Ratio by Sonic Resonance
3. Summary of Test Method
This test method is under the jurisdiction of ASTM Committee C14 on Glass
and Glass Products and is the direct responsibility of Subcommittee C14.04 on
3.1 This test method measures the resonance frequencies of
Physical and Mechanical Properties.
test bars of suitable geometry by exciting them at continuously
CurrenteditionapprovedJune1,2021.PublishedJuly2021.Originallyapproved
in 1969. Last previous edition approved in 2015 as C623–92(2015). DOI:
10.1520/C0623-21. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Spinner,S.andTefft,W.E.,“AMethodforDeterminingMechanicalResonance contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
Frequencies and for Calculating Elastic Moduli From These Frequencies,” Standards volume information, refer to the standard’s Document Summary page on
Proceedings, ASTM International, 1961, pp. 1221–1238. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
C623 − 21
FIG. 1 Block Diagram of Apparatus
variable frequencies. Mechanical excitation of the specimen is convert the electrical signal to a mechanical driving vibration.
provided through use of a transducer that transforms an initial A frequency meter monitors the audio oscillator output to
electrical signal into a mechanical vibration. Another trans- provide an accurate frequency determination. A suitable
ducer senses the resulting mechanical vibrations of the speci- suspension-coupling system cradles the test specimen, and
men and transforms them into an electrical signal that can be another transducer acts to detect mechanical resonance in the
displayed on the screen of an oscilloscope to detect resonance. specimen and to convert it into an electrical signal which is
The resonance frequencies, dimensions, and mass of the passedthroughanamplifieranddisplayedontheverticalplates
specimen are used to calculateYoung’s modulus and the shear ofanoscilloscope.IfaLissajousfigureisdesired,theoutputof
modulus. the oscillator is also coupled to the horizontal plates of the
oscilloscope. If temperature-dependent data are desired, a
4. Significance and Use
suitable furnace or cryogenic chamber is used. Details of the
equipment are as follows:
4.1 This test system has advantages in certain respects over
the use of static loading systems in the measurement of glass
5.2 Audio Oscillator, having a continuously variable fre-
and glass-ceramics:
quencyoutputfromabout100Hztoatleast20kHz.Frequency
4.1.1 Only minute stresses are applied to the specimen, thus
drift shall not exceed 1 Hz/min for any given setting.
minimizing the possibility of fracture.
5.3 Audio Amplifier, having a power output sufficient to
4.1.2 The period of time during which stress is applied and
ensurethatthetypeoftransducerusedcanexciteanyspecimen
removed is of the order of hundreds of microseconds, making
the mass of which falls within a specified range.
it feasible to perform measurements at temperatures where
5.4 Transducers—Two are required: one used as a driver
delayed elastic and creep effects proceed on a much-shortened
maybeaspeakerofthetweetertypeoramagneticcuttinghead
timescale,asinthetransformationrangeofglass,forinstance.
or other similar device, depending on the type of coupling
4.2 The test is suitable for detecting whether a material
chosen for use between the transducer and the specimen. The
meets specifications, if cognizance is given to one important
other transducer, used as a detector, may be a crystal or
fact: glass and glass-ceramic materials are sensitive to thermal
magneticreluctancetypeofphonographcartridge.Acapacitive
history. Therefore the thermal history of a test specimen must
pickup may be used if desired. The frequency response of the
be known before the moduli can be considered in terms of
transducer shall be as good as possible with at least a 6.5kHz
specified values. Material specifications should include a
bandwidth before 3-dB power loss occurs.
specific thermal treatment for all test specimens.
5.5 Power Amplifier, in the detector circuit shall be imped-
5. Apparatus ance matched with the type of detector transducer selected and
shall serve as a prescope amplifier.
5.1 The test apparatus is shown in Fig. 1. It consists of a
variable-frequency audio oscillator, used to generate a sinusoi- 5.6 Oscilloscope, shall be any model suitable for general
dal voltage, and a power amplifier and suitable transducer to laboratory work.
C623 − 21
FIG. 3 Specimen Positioned for Measurement of Flexural and
Torsional Resonance Frequencies Using Thread or Wire Suspen-
sion
1—Cylindrical glass jar
2—Glass wool
6. Test Specimen
3—Plastic foam
4—Vacuum jar
6.1 The specimens shall be prepared so that they are either
5—Heater disk
rectangular or circular in cross section. Either geometry can be
6—Copper plate
used to measure both Young’s modulus and shear modulus.
7—Thermocouple
8—Sample
However, great experimental difficulties in obtaining torsional
9—Suspension wires
resonance frequencies for a cylindrical specimen usually pre-
10—Fill port for liquid
clude its use in determining shear modulus, although the
FIG. 2 Detail Drawing of Suitable Cryogenic Chamber
equations for computing shear modulus with a cylindrical
specimen are both simpler and more accurate than those used
with a prismatic bar.
5.7 Frequency Counter,shallbeabletomeasurefrequencies
to within 61Hz. 6.2 Resonance frequencies for a given specimen are func-
tions of the bar dimensions as well as its density and modulus;
5.8 If data at elevated temperature are desired, a furnace
therefore, dimensions should be selected with this relationship
shall be used that is capable of controlled heating and cooling.
in mind. Selection of size shall be made so that, for an
It shall have a specimen zone 180 mm in length, which will be
estimated modulus, the resonance frequencies measured will
uniform in temperature within 65°C throughout the range of
fall within the range of frequency response of the transducers
temperatures encountered in testing.
used. Representative values of Young’s modulus are
4 2 4 2
5.9 For data at cryogenic temperatures, any chamber shall
70×10 kgf⁄cm (69 GPa) for glass and 100×10 kgf⁄cm
suffice that shall be capable of controlled heating, frost-free,
(98GPa)forglass-ceramics.Recommendedspecimensizesare
anduniformintemperaturewithin 65°Coverthelengthofthe
120 by 25 by 3 mm for bars of rectangular cross section, and
specimen at any selected temperature. A suitable cryogenic
120 by 4mm for those of circular cross section. These
chamber is shown in Fig. 2.
specimen sizes should produce a fundamental flexural reso-
5.10 Any method of specimen suspension shall be used that nance frequency in the range from 1000 to 2000 Hz. Speci-
mens shall have a minimum mass of5gto avoid coupling
shall be adequate for the temperatures encountered in testing
and that shall allow the specimen to vibrate without significant effects; any size of specimen that has a suitable length-to-cross
sectionratiointermsoffrequencyresponseandmeetsthemass
restriction. Common cotton thread, silica glass fiber thread,
Nichrome, or platinum wire may be used. If metal wire minimum may be used. Maximum specimen size and mass are
determined primarily by the test system’s energy and space
suspension is used in the furnace, coupling characteristics will
be improved if, outside the temperature zone, the wire is capabilities.
coupled to cotton thread and the thread is coupled to the
6.3 Specimensshallbefinishedusingafinegrind,–400-grit
transducer. If specimen supports of other than the suspension
or smaller.All surfaces shall be flat and opposite surfaces shall
type are used, they shall meet the same general specifications.
be parallel within 0.02 mm.
7. Procedure
Smith,R.E.andHagy,H.E.,“ALowTemperatureSonicResonanceApparatus
7.1 Procedure A—Room Temperature Testing—Position the
for Determining Elastic Properties of Solids,” Internal Report 2195, Corning Glass
Works, April 1961. specimen properly (see Figs. 3 and 4).Activate the equipment
C623 − 21
FIG. 4 Specimen Positioned for Measurement of Flexural and
Torsional Resonance Frequencies Using “Tweeter” Exciter
FIG. 5 Some Modes of Mechanical Vibration in Bar
so that power adequate to excite the specimen is delivered to
the driving transducer. Set the gain of the detector circuit high
fundamental in flexure when computingYoung’s modulus for a rectangu-
enough to detect vibration in the specimen and to display it on larbarbecauseoftheapproximatenatureofPickett’stheory.However,for
the nominal size of bar specified, the values of Young’s modulus
the oscilloscope screen with sufficient amplitude to measure
computedusingEq1andEq2willagreewithin1%.Whenthecorrection
accurately the frequency at which the signal amplitude is
factor, T , is greater than 2%, Eq 2 sho
...

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: C623 − 92 (Reapproved 2015) C623 − 21
Standard Test Method for
Young’s Modulus, Shear Modulus, and Poisson’s Ratio for
Glass and Glass-Ceramics by Resonance
This standard is issued under the fixed designation C623; 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 elastic properties of glass and glass-ceramic materials. Specimens of these
materials possess specific mechanical resonance frequencies which are defined by the elastic moduli, density, and geometry of the
test specimen. Therefore the elastic properties of a material can be computed if the geometry, density, and mechanical resonance
frequencies of a suitable test specimen of that material can be measured. Young’s modulus is determined using the resonance
frequency in the flexural mode of vibration. The shear modulus, or modulus of rigidity, is found using torsional resonance
vibrations. Young’s modulus and shear modulus are used to compute Poisson’s ratio, the factor of lateral contraction.
1.2 All glass and glass-ceramic materials that are elastic, homogeneous, and isotropic may be tested by this test method. The test
method is not satisfactory for specimens that have cracks or voids that represent inhomogeneities in the material; neither is it
satisfactory when these materials cannot be prepared in a suitable geometry. Non-glass and glass-ceramic materials should
reference Test Method E1875 for non-material specific methodology to determine resonance frequencies and elastic properties by
sonic resonance.
NOTE 1—Elastic here means that an application of stress within the elastic limit of that material making up the body being stressed will cause an
instantaneous and uniform deformation, which will cease upon removal of the stress, with the body returning instantly to its original size and shape
without an energy loss. Glass and glass-ceramic materials conform to this definition well enough that this test is meaningful.
NOTE 2—Isotropic means that the elastic properties are the same in all directions in the material. Glass is isotropic and glass-ceramics are usually so on
a macroscopic scale, because of random distribution and orientation of crystallites.
1.3 A cryogenic cabinet and high-temperature furnace are described for measuring the elastic moduli as a function of temperature
from –195 to 1200°C.1200 °C.
1.4 Modification of the test for use in quality control is possible. A range of acceptable resonance frequencies is determined for
a piece with a particular geometry and density. Any specimen with a frequency response falling outside this frequency range is
rejected. The actual modulus of each piece need not be determined as long as the limits of the selected frequency range are known
to include the resonance frequency that the piece must possess if its geometry and density are within specified tolerances.
1.5 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
This test method is under the jurisdiction of ASTM Committee C14 on Glass and Glass Products and is the direct responsibility of Subcommittee C14.04 on Physical
and Mechanical Properties.
Current edition approved May 1, 2015June 1, 2021. Published May 2015July 2021. Originally approved in 1969. Last previous edition approved in 20102015 as C623 – 92
(2010).(2015). DOI: 10.1520/C0623-92R15.10.1520/C0623-21.
Spinner, S.,S. and Tefft, W. E., “A Method for Determining Mechanical Resonance Frequencies and for Calculating Elastic Moduli fromFrom These Frequencies,”
Proceedings, ASTM, ASTM International, 1961, pp. 1221–1238.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
C623 − 21
1.6 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.
1.7 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
2.1 Reference to these documents shall be the latest issue unless otherwise specified by the authority applying this test method.
2.2 ASTM Standards:
E1875 Test Method for Dynamic Young’s Modulus, Shear Modulus, and Poisson’s Ratio by Sonic Resonance
3. Summary of Test Method
3.1 This test method measures the resonance frequencies of test bars of suitable geometry by exciting them at continuously
variable frequencies. Mechanical excitation of the specimen is provided through use of a transducer that transforms an initial
electrical signal into a mechanical vibration. Another transducer senses the resulting mechanical vibrations of the specimen and
transforms them into an electrical signal that can be displayed on the screen of an oscilloscope to detect resonance. The
reasonanceresonance frequencies, the dimensions, and the mass of the specimen are used to calculate Young’s modulus and the
shear modulus.
4. Significance and Use
4.1 This test system has advantages in certain respects over the use of static loading systems in the measurement of glass and
glass-ceramics:
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.
C623 − 21
4.1.1 Only minute stresses are applied to the specimen, thus minimizing the possibility of fracture.
4.1.2 The period of time during which stress is applied and removed is of the order of hundreds of microseconds, making it
feasible to perform measurements at temperatures where delayed elastic and creep effects proceed on a much-shortened time scale,
as in the transformation range of glass, for instance.
FIG. 1 Block Diagram of Apparatus
4.2 The test is suitable for detecting whether a material meets specifications, if cognizance is given to one important fact: glass
and glass-ceramic materials are sensitive to thermal history. Therefore the thermal history of a test specimen must be known before
the moduli can be considered in terms of specified values. Material specifications should include a specific thermal treatment for
all test specimens.
5. Apparatus
5.1 The test apparatus is shown in Fig. 1. It consists of a variable-frequency audio oscillator, used to generate a sinusoidal voltage,
and a power amplifier and suitable transducer to convert the electrical signal to a mechanical driving vibration. A frequency meter
monitors the audio oscillator output to provide an accurate frequency determination. A suitable suspension-coupling system cradles
the test specimen, and another transducer acts to detect mechanical resonance in the specimen and to convert it into an electrical
signal which is passed through an amplifier and displayed on the vertical plates of an oscilloscope. If a Lissajous figure is desired,
the output of the oscillator is also coupled to the horizontal plates of the oscilloscope. If temperature-dependent data are desired,
a suitable furnace or cryogenic chamber is used. Details of the equipment are as follows:
5.2 Audio Oscillator, having a continuously variable frequency output from about 100 Hz to at least 20 kHz. Frequency drift shall
not exceed 1 Hz/min for any given setting.
5.3 Audio Amplifier, having a power output sufficient to ensure that the type of transducer used can excite any specimen the mass
of which falls within a specified range.
5.4 Transducers—Two are required: one used as a driver may be a speaker of the tweeter type or a magnetic cutting head or other
similar device, depending on the type of coupling chosen for use between the transducer and the specimen. The other transducer,
C623 − 21
1—Cylindrical glass jar
2—Glass wool
3—Plastic foam
4—Vacuum jar
5—Heater disk
6—Copper plate
7—Thermocouple
8—Sample
9—Suspension wires
10—Fill port for liquid
FIG. 2 Detail Drawing of Suitable Cryogenic Chamber
used as a detector, may be a crystal or magnetic reluctance type of phonograph cartridge. A capacitive pickup may be used if
desired. The frequency response of the transducer shall be as good as possible with at least a 6.5 kHz bandwidth before 3-dB power
loss occurs.
5.5 Power Amplifier, in the detector circuit shall be impedance matched with the type of detector transducer selected and shall
serve as a prescope amplifier.
5.6 Cathode-Ray Oscilloscope, shall be any model suitable for general laboratory work.
5.7 Frequency Counter, shall be able to measure frequencies to within 61 Hz.
5.8 If data at elevated temperature are desired, a furnace shall be used that is capable of controlled heating and cooling. It shall
have a specimen zone 180 mm in length, which will be uniform in temperature within 65°C65 °C throughout the range of
temperatures encountered in testing.
5.9 For data at cryogenic temperatures, any chamber shall suffice that shall be capable of controlled heating, frost-free, and
uniform in temperature within 65°C65 °C over the length of the specimen at any selected temperature. A suitable cryogenic
chamber is shown in Fig. 2.
5.10 Any method of specimen suspension shall be used that shall be adequate for the temperatures encountered in testing and that
shall allow the specimen to vibrate without significant restriction. Common cotton thread, silica glass fiber thread, Nichrome, or
platinum wire may be used. If metal wire suspension is used in the furnace, coupling characteristics will be improved if, outside
Smith, R. E.,E. and Hagy, H. E., “A Low Temperature Sonic Resonance Apparatus for Determining Elastic Properties of Solids,” Internal Report 2195, Corning Glass
Works, April,April 1961.
C623 − 21
FIG. 3 Specimen Positioned for Measurement of Flexural and Torsional Resonance Frequencies Using Thread or Wire Suspension
the temperature zone, the wire is coupled to cotton thread and the thread is coupled to the transducer. If specimen supports of other
than the suspension type are used, they shall meet the same general specifications.
6. Test Specimen
6.1 The specimens shall be prepared so that they are either rectangular or circular in cross section. Either geometry can be used
to measure both Young’s modulus and shear modulus. However, great experimental difficulties in obtaining torsional resonance
frequencies for a cylindrical specimen usually preclude its use in determining shear modulus, although the equations for computing
shear modulus with a cylindrical specimen are both simpler and more accurate than those used with a prismatic bar.
6.2 Resonance frequencies for a given specimen are functions of the bar dimensions as well as its density and modulus; therefore,
dimensions should be selected with this relationship in mind. Selection of size shall be made so that, for an estimated modulus,
the resonance frequencies measured will fall within the range of frequency response of the transducers used. Representative values
4 2 4 2
of Young’s modulus are 70 × 10 kgf ⁄cm (69 GPa) for glass and 100 × 10 kgf ⁄cm (98 GPa) for glass-ceramics. Recommended
specimen sizes are 120 by 25 by 3 mm for bars of rectangular cross section, and 120 by 4 mm for those of circular cross section.
These specimen sizes should produce a fundamental flexural resonance frequency in the range from 1000 to 2000 Hz. Specimens
shall have a minimum mass of 5 g to avoid coupling effects; any size of specimen that has a suitable length-to-cross section ratio
in terms of frequency response and meets the mass minimum may be used. Maximum specimen size and mass are determined
primarily by the test system’s energy and space capabilities.
6.3 Specimens shall be finished using a fine grind –400-gritgrind, –400-grit or smaller. All surfaces shall be flat and opposite
surfaces shall be parallel within 0.02 mm.
7. Procedure
7.1 Procedure A—Room Temperature Testing—Position the specimen properly (see Figs. 3 and 4). Activate the equipment so that
power adequate to excite the specimen is delivered to the driving transducer. Set the gain of the detector circuit high enough to
detect vibration in the specimen and to display it on the oscilloscope screen with sufficient amplitude to measure accurately the
frequency at which the signal amplitude is maximized. Adjust the oscilloscope so that a sharply defined horizontal baseline exists
when the specimen is not excited. Scan frequencies with the audio oscillator until specimen resonance is indicated by a sinusoidal
pattern of maximum amplitude on the oscilloscope. Find the fundamental mode of vibration in flexure, then find the first overtone
in flexture (Note 3). Establish definitely the fundamental flexural mode by positioning the detector at the appropriate nodal position
of the specimen (see Fig. 5). At this point the amplitude of the resonance signal will decrease to zero. The ratio of the first overtone
frequency to the fundamental frequency will be approximately 2.70 to 2.75. If a determination of the shear modulus is to be made,
offset the coupling to the tran
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