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

SIGNIFICANCE AND USE
This test system has advantages in certain respects over the use of static loading systems in the measurement of glass and glass-ceramics:  
Only minute stresses are applied to the specimen, thus minimizing the possibility of fracture.
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.
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. 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°C 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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ASTM C623-92(2010) - Standard Test Method for Young's Modulus, Shear Modulus, and Poisson's Ratio for Glass and Glass-Ceramics by Resonance
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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: C623 − 92(Reapproved 2010)
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°C 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 April 1, 2010. Published May 2010. Originally
approved in 1969. Last previous edition approved in 2005 as C623–92(2005).
removed is of the order of hundreds of microseconds, making
DOI: 10.1520/C0623-92R10.
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 (2010)
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 6.5-kHz
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 61 Hz.
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 (2010)
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
termsoffrequencyresponseandmeetsthemassminimummay
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 Fig. 3 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
1—Cylindrical glass jar
2—Glass wool sharplydefinedhorizontalbaselineexistswhenthespecimenis
3—Plastic foam
not excited. Scan frequencies with the audio oscillator until
4—Vacuum jar
specimen resonance is indicated by a sinusoidal pattern of
5—Heater disk
6—Copper plate maximumamplitudeontheoscilloscope.Findthefundamental
7—Thermocouple
mode of vibration in flexure, then find the first overtone in
8—Sample
flexture (Note 3). Establish definitely the fundamental flexural
9—Suspension wires
10—Fill port for liquid
mode by positioning the detector at the appropriate nodal
FIG. 2 Detail Drawing of Suitable Cryogenic Chamber
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
restriction. Common cotton thread, silica glass fiber thread,
Nichrome, or platinum wire may be used. If metal wire frequency will be approximately 2.70 to 2.75. If a determina-
tion of the shear modulus is to be made, offset the coupling to
suspension is used in the furnace, coupling characteristics will
be improved if, outside the temperature zone, the wire is the transducers so that the torsional mode of vibration may be
detected(seeFig.3).Findthefundamentalresonancevibration
coupled to cotton thread and the thread is coupled to the
transducer. If specimen supports of other than the suspension in this mode. Identify the torsional mode by centering the
detector with respect to the width of the specimen and
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 70×10
4 2
kgf/cm (69GPa)forglassand100×10 kgf/cm (98GPa)for
FIG. 3 Specimen Positioned for Measurement of Flexural and
glass-ceramics. Recommended specimen sizes are 120 by 25
Torsional Resonance Frequencies Using Thread or Wire Suspen-
by 3 mm for bars of rectangular cross section, and 120 by 4 sion
C623 − 92 (2010)
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,
etc., 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 15-min 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
ch
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