ASTM C623-92(2015)
(Test Method)Standard Test Method for Young's Modulus, Shear Modulus, and Poisson's Ratio for Glass and Glass-Ceramics by Resonance
Standard Test Method for Young's Modulus, Shear Modulus, and Poisson's Ratio for Glass and Glass-Ceramics by Resonance
SIGNIFICANCE AND USE
3.1 This test system has advantages in certain respects over the use of static loading systems in the measurement of glass and glass-ceramics:
3.1.1 Only minute stresses are applied to the specimen, thus minimizing the possibility of fracture.
3.1.2 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.
3.2 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.
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 and health practices and determine the applicability of regulatory limitations prior to use.
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Designation: C623 − 92 (Reapproved 2015)
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 1.4 Modification of the test for use in quality control is
possible. A range of acceptable resonance frequencies is
1.1 This test method covers the determination of the elastic
determined for a piece with a particular geometry and density.
properties of glass and glass-ceramic materials. Specimens of
Any specimen with a frequency response falling outside this
thesematerialspossessspecificmechanicalresonancefrequen-
frequency range is rejected. The actual modulus of each piece
cies which are defined by the elastic moduli, density, and
need not be determined as long as the limits of the selected
geometry of the test specimen. Therefore the elastic properties
frequency range are known to include the resonance frequency
of a material can be computed if the geometry, density, and
that the piece must possess if its geometry and density are
mechanical resonance frequencies of a suitable test specimen
within specified tolerances.
of that material can be measured. Young’s modulus is deter-
1.5 The values stated in SI units are to be regarded as
mined using the resonance frequency in the flexural mode of
standard. No other units of measurement are included in this
vibration. The shear modulus, or modulus of rigidity, is found
standard.
using torsional resonance vibrations. Young’s modulus and
shear modulus are used to compute Poisson’s ratio, the factor
1.6 This standard does not purport to address all of the
of lateral contraction.
safety concerns, if any, associated with its use. It is the
responsibility of the user of this standard to establish appro-
1.2 All glass and glass-ceramic materials that are elastic,
priate safety and health practices and determine the applica-
homogeneous,andisotropicmaybetestedbythistestmethod.
bility of regulatory limitations prior to use.
The test method is not satisfactory for specimens that have
cracks or voids that represent inhomogeneities in the material;
2. Summary of Test Method
neither is it satisfactory when these materials cannot be
2.1 This test method measures the resonance frequencies of
prepared in a suitable geometry.
test bars of suitable geometry by exciting them at continuously
NOTE 1—Elastic here means that an application of stress within the
variable frequencies. Mechanical excitation of the specimen is
elastic limit of that material making up the body being stressed will cause
provided through use of a transducer that transforms an initial
aninstantaneousanduniformdeformation,whichwillceaseuponremoval
electrical signal into a mechanical vibration. Another trans-
ofthestress,withthebodyreturninginstantlytoitsoriginalsizeandshape
without an energy loss. Glass and glass-ceramic materials conform to this
ducer senses the resulting mechanical vibrations of the speci-
definition well enough that this test is meaningful.
men and transforms them into an electrical signal that can be
NOTE 2—Isotropic means that the elastic properties are the same in all
displayed on the screen of an oscilloscope to detect resonance.
directionsinthematerial.Glassisisotropicandglass-ceramicsareusually
The reasonance frequencies, the dimensions, and the mass of
so on a macroscopic scale, because of random distribution and orientation
the specimen are used to calculate Young’s modulus and the
of crystallites.
shear modulus.
1.3 A cryogenic cabinet and high-temperature furnace are
described for measuring the elastic moduli as a function of
3. Significance and Use
temperature from–195 to 1200°C.
3.1 This test system has advantages in certain respects over
the use of static loading systems in the measurement of glass
and glass-ceramics:
This test method is under the jurisdiction of ASTM Committee C14 on Glass
3.1.1 Only minute stresses are applied to the specimen, thus
and Glass Products and is the direct responsibility of Subcommittee C14.04 on
minimizing the possibility of fracture.
Physical and Mechanical Properties.
3.1.2 The period of time during which stress is applied and
Current edition approved May 1, 2015. Published May 2015. Originally
approved in 1969. Last previous edition approved in 2010 as C623–92(2010).
removed is of the order of hundreds of microseconds, making
DOI: 10.1520/C0623-92R15.
it feasible to perform measurements at temperatures where
Spinner, S., and Tefft, W. E., “A Method for Determining Mechanical
delayed elastic and creep effects proceed on a much-shortened
Resonance Frequencies and for Calculating Elastic Moduli from These
Frequencies,” Proceedings, ASTM, 1961, pp. 1221–1238. timescale,asinthetransformationrangeofglass,forinstance.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
C623 − 92 (2015)
FIG. 1 Block Diagram of Apparatus
3.2 The test is suitable for detecting whether a material or other similar device, depending on the type of coupling
meets specifications, if cognizance is given to one important chosen for use between the transducer and the specimen. The
fact: glass and glass-ceramic materials are sensitive to thermal other transducer, used as a detector, may be a crystal or
history. Therefore the thermal history of a test specimen must magneticreluctancetypeofphonographcartridge.Acapacitive
be known before the moduli can be considered in terms of pickup may be used if desired. The frequency response of the
specified values. Material specifications should include a transducer shall be as good as possible with at least a 6.5kHz
specific thermal treatment for all test specimens. bandwidth before 3-dB power loss occurs.
4.5 Power Amplifier, in the detector circuit shall be imped-
4. Apparatus
ance matched with the type of detector transducer selected and
4.1 The test apparatus is shown in Fig. 1. It consists of a
shall serve as a prescope amplifier.
variable-frequency audio oscillator, used to generate a sinusoi-
4.6 Cathode-Ray Oscilloscope, shall be any model suitable
dal voltage, and a power amplifier and suitable transducer to
for general laboratory work.
convert the electrical signal to a mechanical driving vibration.
4.7 Frequency Counter,shallbeabletomeasurefrequencies
A frequency meter monitors the audio oscillator output to
to within 61Hz.
provide an accurate frequency determination. A suitable
suspension-coupling system cradles the test specimen, and
4.8 If data at elevated temperature are desired, a furnace
another transducer acts to detect mechanical resonance in the
shall be used that is capable of controlled heating and cooling.
specimen and to convert it into an electrical signal which is
It shall have a specimen zone 180 mm in length, which will be
passedthroughanamplifieranddisplayedontheverticalplates
uniform in temperature within 65°C throughout the range of
ofanoscilloscope.IfaLissajousfigureisdesired,theoutputof
temperatures encountered in testing.
the oscillator is also coupled to the horizontal plates of the
4.9 For data at cryogenic temperatures, any chamber shall
oscilloscope. If temperature-dependent data are desired, a
suffice that shall be capable of controlled heating, frost-free,
suitable furnace or cryogenic chamber is used. Details of the
anduniformintemperaturewithin 65°Coverthelengthofthe
equipment are as follows:
specimen at any selected temperature. A suitable cryogenic
4.2 Audio Oscillator, having a continuously variable fre-
chamber is shown in Fig. 2.
quencyoutputfromabout100Hztoatleast20kHz.Frequency
4.10 Any method of specimen suspension shall be used that
drift shall not exceed 1 Hz/min for any given setting.
shall be adequate for the temperatures encountered in testing
4.3 Audio Amplifier, having a power output sufficient to
and that shall allow the specimen to vibrate without significant
ensurethatthetypeoftransducerusedcanexciteanyspecimen
the mass of which falls within a specified range.
Smith, R. E., and Hagy, H. E., “A Low Temperature Sonic Resonance
4.4 Transducers—Two are required: one used as a driver
Apparatus for Determining Elastic Properties of Solids,” Internal Report 2195,
maybeaspeakerofthetweetertypeoramagneticcuttinghead Corning Glass Works, April, 1961.
C623 − 92 (2015)
120 by 4mm for those of circular cross section. These
specimen sizes should produce a fundamental flexural reso-
nance frequency in the range from 1000 to 2000 Hz. Speci-
mens shall have a minimum mass of5gto avoid coupling
effects; any size of specimen that has a suitable length-to-cross
sectionratiointermsoffrequencyresponseandmeetsthemass
minimum may be used. Maximum specimen size and mass are
determined primarily by the test system’s energy and space
capabilities.
5.3 Specimens shall be finished using a fine grind–400-grit
or smaller.All surfaces shall be flat and opposite surfaces shall
be parallel within 0.02 mm.
6. Procedure
6.1 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
1—Cylindrical glass jar
2—Glass wool maximized. Adjust the oscilloscope so that a sharply defined
3—Plastic foam
horizontal baseline exists when the specimen is not excited.
4—Vacuum jar
Scan frequencies with the audio oscillator until specimen
5—Heater disk
6—Copper plate resonance is indicated by a sinusoidal pattern of maximum
7—Thermocouple
amplitude on the oscilloscope. Find the fundamental mode of
8—Sample
vibration in flexure, then find the first overtone in flexture
9—Suspension wires
10—Fill port for liquid
(Note3).Establishdefinitelythefundamentalflexuralmodeby
FIG. 2 Detail Drawing of Suitable Cryogenic Chamber
positioningthedetectorattheappropriatenodalpositionofthe
specimen (see Fig. 5). At this point the amplitude of the
resonance signal will decrease to zero. The ratio of the first
restriction. Common cotton thread, silica glass fiber thread,
Nichrome, or platinum wire may be used. If metal wire overtone frequency to the fundamental frequency will be
approximately 2.70 to 2.75. If a determination of the shear
suspension is used in the furnace, coupling characteristics will
be improved if, outside the temperature zone, the wire is modulusistobemade,offsetthecouplingtothetransducersso
that the torsional mode of vibration may be detected (see Fig.
coupled to cotton thread and the thread is coupled to the
transducer. If specimen supports of other than the suspension 3). Find the fundamental resonance vibration in this mode.
Identify the torsional mode by centering the detector with
type are used, they shall meet the same general specifications.
5. Test Specimen
5.1 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 pre-
clude 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.
5.2 Resonance frequencies for a given specimen are func-
tions 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 of Young’s modulus are
4 2 4 2
70×10 kgf⁄cm (69 GPa) for glass and 100×10 kgf⁄cm
FIG. 3 Specimen Positioned for Measurement of Flexural and
(98GPa)forglass-ceramics.Recommendedspecimensizesare
Torsional Resonance Frequencies Using Thread or Wire Suspen-
120 by 25 by 3 mm for bars of rectangular cross section, and sion
C623 − 92 (2015)
The fundamental and overtone are properly identified by showing them to
be in the correct numerical ratio, and by demonstrating the proper
locations of the nodes for each. Spinner and Tefft recommended using
only the fundamental in flexure when computing Young’s modulus for a
rectangular bar because of the approximate nature of Pickett’s theory.
However, for the nominal size of bar specified, the values of Young’s
modulus computed using Eq 1 and Eq 2 will agree within 1%. When the
correction factor, T , is greater than 2%, Eq 2 should not be used.
6.2 Procedure B—Elevated Temperature Testing—
Determine the mass, dimensions, and frequencies at room
temperature in air as outlined in 6.1. Place the specimen in the
furnace and adjust the driver-detector system so that all the
frequencies to be measured can be detected without further
adjustment. Determine the resonant frequencies at room tem-
perature in the furnace cavity with the furnace doors closed,
and so forth, as will be the case at elevated temperatures. Heat
the furnace at a controlled rate that does not exceed 150°C/h.
Take data at 25° intervals or at 15min intervals as dictated by
heating rate and specimen composition. Follow the change in
resonance frequencies with time closely to avoid losing the
FIG. 4 Specimen Positioned for Measurement of Flexural and
identity of each frequency. (The overtone in flexure and the
Torsional Resonance Frequencies Using “Tweeter” Exciter
fundamental in torsion may be difficult to differentiate if not
followed closely; spurious frequencies inherent in the system
may also appear at temperatures above 600°C using certain
types of suspensions, particularly wire.) If desired, data may
alsobetakenoncooling;itmustberemembered,however,that
high temperatures may damage the specimen, by serious
warping for example, making subsequent determinations of
doubtful value.
6.3 Procedure C—Cryogenic Temperature Testing—
Determine the weight, dimensions, and resonance frequencies
in air at room temperature. Measure the resonance frequencies
at room temperature in the cryogenic chamber. Take the
chamber to the minimum temperature desired (Note 4),
...
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 2010) C623 − 92 (Reapproved 2015)
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.
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°Cfrom –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 and health practices and determine the applicability of regulatory
limitations prior to use.
2. Summary of Test Method
2.1 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 reasonance
frequencies, the dimensions, and the mass of the specimen are used to calculate Young’s modulus and the shear modulus.
3. Significance and Use
3.1 This test system has advantages in certain respects over the use of static loading systems in the measurement of glass and
glass-ceramics:
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 April 1, 2010May 1, 2015. Published May 2010May 2015. Originally approved in 1969. Last previous edition approved in 20052010 as
C623 – 92 (2005).(2010). DOI: 10.1520/C0623-92R10.10.1520/C0623-92R15.
Spinner, S., and Tefft, W. E., “A Method for Determining Mechanical Resonance Frequencies and for Calculating Elastic Moduli from These Frequencies,” Proceedings,
ASTM, 1961, pp. 1221–1238.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
C623 − 92 (2015)
3.1.1 Only minute stresses are applied to the specimen, thus minimizing the possibility of fracture.
3.1.2 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
3.2 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.
4. Apparatus
4.1 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:
4.2 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.
4.3 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.
4.4 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, 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-kHz6.5 kHz bandwidth
before 3-dB power loss occurs.
4.5 Power Amplifier, in the detector circuit shall be impedance matched with the type of detector transducer selected and shall
serve as a prescope amplifier.
4.6 Cathode-Ray Oscilloscope, shall be any model suitable for general laboratory work.
4.7 Frequency Counter, shall be able to measure frequencies to within 61 Hz.61 Hz.
C623 − 92 (2015)
4.8 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°C throughout the range of temperatures
encountered in testing.
4.9 For data at cryogenic temperatures, any chamber shall suffice that shall be capable of controlled heating, frost-free, and
uniform in temperature within 65°C over the length of the specimen at any selected temperature. A suitable cryogenic chamber
is shown in Fig. 2.
4.10 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
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.
5. Test Specimen
5.1 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.
5.2 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.
4 2 4 2
Representative values of Young’s modulus are 70 × 10 kgf/cm kgf ⁄cm (69 GPa) for glass and 100 × 10 kgf/cm 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 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
Smith, R. E., and Hagy, H. E., “A Low Temperature Sonic Resonance Apparatus for Determining Elastic Properties of Solids,” Internal Report 2195, Corning Glass
Works, April, 1961.
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
C623 − 92 (2015)
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.
5.3 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.
6. Procedure
6.1 Procedure A—Room Temperature Testing—Position the specimen properly (see Fig. 3Figs. 3 and 4 and Fig. 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 transducers so that the torsional mode of vibration may be detected (see
Fig. 3). Find the fundamental resonance vibration in this mode. Identify the torsional mode by centering the detector with respect
to the width of the specimen and observing that the amplitude of the resonance signal decreases to zero; if it does not, the signal
is an overtone of flexure or a spurious frequency generated elsewhere in the system. Dimensions and weight of the specimen may
be measured before or after the test. Measure the dimensions with a micrometer caliper capable of an accuracy of 60.01 mm;
measure the weight with a balance capable of 610 mg accuracy.
NOTE 3—It is recommended that the first overtone in flexure be determined for both rectangular and cylindrical specimens. This is useful in establishing
the proper identification of the fundamental, particularly when spurious frequencies inherent in the system interfere (as, for example, when greater
excitation power and detection sensitivity are required for work with a specimen that has a poor response).
FIG. 3 Specimen Positioned for Measurement of Flexural and Torsional Resonance Frequencies Using Thread or Wire Suspension
C623 − 92 (2015)
FIG. 4 Specimen Positioned for Measurement of Flexural and Torsional Resonance Frequencies Using “Tweeter” Exciter
FIG. 5 Some Modes of Mechanical Vibration in a Bar
The fundamental and overtone are properly identified by showing them to be in the correct numerical ratio, and by demonstrating the proper locations
of the nodes for each. Spinner and Tefft recommended using only the fundamental in flexure when computing Young’s modulus for a rectangular bar
because of the approximate nature of Pickett’s theory. However, for the nominal size of bar specified, the values of Young’s modulus computed using
Eq 1 and
...
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