ASTM C848-88(2006)
(Test Method)Standard Test Method for Young's Modulus, Shear Modulus, and Poisson's Ratio For Ceramic Whitewares by Resonance
Standard Test Method for Young's Modulus, Shear Modulus, and Poisson's Ratio For Ceramic Whitewares by Resonance
SIGNIFICANCE AND USE
This test system has advantages in certain respects over the use of static loading systems in the measurement of ceramic whitewares.
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.
This test method is suitable for detecting whether a material meets specifications, if cognizance is given to one important fact: ceramic whiteware 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 ceramic whiteware 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 ceramic whiteware materials that are elastic, homogeneous, and isotropic may be tested by this test method. This 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 1Elastic 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. Many ceramic whiteware 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.
1.3 A cryogenic cabinet and high-temperature furnace are described for measuring the elastic moduli as a function of temperature from 195 to 1200C.
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.
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:C848–88(Reapproved 2006)
Standard Test Method for
Young’s Modulus, Shear Modulus, and Poisson’s Ratio For
Ceramic Whitewares by Resonance
This standard is issued under the fixed designation C848; 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 ceramic whiteware materials. Specimens of these
1.4 Modification of the test for use in quality control is
materials possess specific mechanical resonance frequencies
possible. A range of acceptable resonance frequencies is
which are defined by the elastic moduli, density, and geometry
determined for a piece with a particular geometry and density.
of the test specimen. Therefore the elastic properties of a
Any specimen with a frequency response falling outside this
material can be computed if the geometry, density, and me-
frequency range is rejected. The actual modulus of each piece
chanical resonance frequencies of a suitable test specimen of
need not be determined as long as the limits of the selected
that material can be measured.Young’s modulus is determined
frequency range are known to include the resonance frequency
using the resonance frequency in the flexural mode of vibra-
that the piece must possess if its geometry and density are
tion.The shear modulus, or modulus of rigidity, is found using
within specified tolerances.
torsional resonance vibrations. Young’s modulus and shear
1.5 This standard does not purport to address all of the
modulus are used to compute Poisson’s ratio, the factor of
safety concerns, if any, associated with its use. It is the
lateral contraction.
responsibility of the user of this standard to establish appro-
1.2 All ceramic whiteware materials that are elastic, homo-
priate safety and health practices and determine the applica-
geneous,andisotropicmaybetestedbythistestmethod. This
bility of regulatory limitations prior to use.
test method is not satisfactory for specimens that have cracks
or voids that represent inhomogeneities in the material; neither
2. Summary of Test Method
is it satisfactory when these materials cannot be prepared in a
2.1 This test method measures the resonance frequencies of
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
ducer senses the resulting mechanical vibrations of the speci-
withoutanenergyloss.Manyceramicwhitewarematerialsconformtothis
men and transforms them into an electrical signal that can be
definition well enough that this test is meaningful.
NOTE 2—Isotropic means that the elastic properties are the same in all
displayed on the screen of an oscilloscope to detect resonance.
directions in the material.
Theresonancefrequencies,thedimensions,andthemassofthe
specimen are used to calculateYoung’s modulus and the shear
modulus.
ThistestmethodisunderthejurisdictionofASTMCommitteeC21onCeramic
Whitewares and Related Products and is the direct responsibility of Subcommittee
3. Significance and Use
C21.03 on Methods for Whitewares and Environmental Concerns.
3.1 This test system has advantages in certain respects over
Current edition approved Feb. 15, 2006. Published February 2006. Originally
approved in 1976. Last previous edition approved in 1999 as C848–88 (1999).
theuseofstaticloadingsystemsinthemeasurementofceramic
DOI: 10.1520/C0848-88R06.
whitewares.
Spinner, S., and Tefft, W. E., “A Method for Determining Mechanical
3.1.1 Only minute stresses are applied to the specimen, thus
Resonance Frequencies and for Calculating Elastic Moduli from These Frequen-
cies,” Proceedings, ASTM, 1961, pp. 1221–1238. minimizing the possibility of fracture.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
C848–88 (2006)
FIG. 1 Block Diagram of Apparatus
3.1.2 The period of time during which stress is applied and 4.3 Audio Amplifier, having a power output sufficient to
removed is of the order of hundreds of microseconds, making ensurethatthetypeoftransducerusedcanexciteanyspecimen
the mass of which falls within a specified range.
it feasible to perform measurements at temperatures where
delayed elastic and creep effects proceed on a much-shortened
4.4 Transducers—Two are required; one used as a driver
time scale.
maybeaspeakerofthetweetertypeoramagneticcuttinghead
or other similar device, depending on the type of coupling
3.2 This test method is suitable for detecting whether a
chosen for use between the transducer and the specimen. The
material meets specifications, if cognizance is given to one
other transducer, used as a detector, may be a crystal or
important fact: ceramic whiteware materials are sensitive to
magneticreluctancetypeofphonographcartridge.Acapacitive
thermal history. Therefore, the thermal history of a test
pickup may be used if desired. The frequency response of the
specimen must be known before the moduli can be considered
transducer shall be as good as possible with at least a 6.5-kHz
in terms of specified values. Material specifications should
bandwidth before 3-dB power loss occurs.
include a specific thermal treatment for all test specimens.
4.5 Power Amplifier, in the detector circuit shall be imped-
ance matched with the type of detector transducer selected and
4. Apparatus
shall serve as a prescope amplifier.
4.1 The test apparatus is shown in Fig. 1. It consists of a
4.6 Cathode-Ray Oscilloscope, shall be any model suitable
variable-frequency audio oscillator, used to generate a sinusoi-
for general laboratory work.
dal voltage, and a power amplifier and suitable transducer to
4.7 Frequency Counter, shall be able to measure frequen-
convert the electrical signal to a mechanical driving vibration.
cies to within 61 Hz.
A frequency meter monitors the audio oscillator output to
4.8 If data at elevated temperatures are desired, a furnace
provide an accurate frequency determination. A suitable
shall be used that is capable of controlled heating and cooling.
suspension-coupling system cradles the test specimen, and
It shall have a specimen zone 180 mm in length, which will be
another transducer acts to detect mechanical resonance in the
uniform in temperature within 65°C throughout the range of
specimen and to convert it into an electrical signal which is
temperatures encountered in testing.
passedthroughanamplifieranddisplayedontheverticalplates
ofanoscilloscope.IfaLissajousfigureisdesired,theoutputof 4.9 For data at cryogenic temperatures, any chamber shall
the oscillator is also coupled to the horizontal plates of the
suffice that is capable of controlled heating, frost-free, and
oscilloscope. If temperature-dependent data are desired, a uniform in temperature within 65°C over the length of the
suitable furnace or cryogenic chamber is used. Details of the
equipment are as follows:
4.2 Audio Oscillator, having a continuously variable fre-
quency output from about 100 to at least 20 kHz. Frequency
drift shall not exceed 1 Hz/min for any given setting.
C848–88 (2006)
FIG. 3 Specimen Positioned for Measurement of Flexural and
Torsional Resonance Frequencies Using Thread or Wire
Suspension
1—Cylindrical glass jar
2—Glass wool
in mind. Make selection of size so that, for anestimated
3—Plastic foam
modulus, the resonance frequencies measured will fall within
4—Vacuum jar
5—Heater disk
the range of frequency response of the transducers used.
6—Copper plate 6
Representative values of Young’s modulus are 10 310 psi
7—Thermocouple
(69 GPa) for vitreous triaxial porcelains and 32 310 psi (220
8—Sample
9—Suspension wires
GPa) for 85% alumina porcelains. Recommended specimen
10—Fill port for liquid
sizes are 125 by 15 by 6 mm for bars of rectangular cross
FIG. 2 Detail Drawing of Suitable Cryogenic Chamber
section and 125 by 10 to 12 mm for those of circular cross
section. These specimen sizes should produce a fundamental
specimen at any selected temperature. A suitable cryogenic
flexural resonance frequency in the range from 1000 to 2000
chamber is shown in Fig. 2.
Hz. Specimens shall have a minimum mass of5gto avoid
4.10 Any method of specimen suspension shall be used that
coupling effects: any size of specimen that has a suitable
isadequateforthetemperaturesencounteredintestingandthat
length-to-crosssectionratiointermsoffrequencyresponseand
shall allow the specimen to vibrate without significant restric-
meets the mass minimum may be used. Maximum specimen
tion. Common cotton thread, silica glass fiber thread,
size and mass are determined primarily by the test system’s
Nichrome, or platinum wire may be used. If metal wire
energy and space capabilities.
suspension is used in the furnace, coupling characteristics will
5.3 Finish specimens using a fine grind, 400 grit or smaller.
be improved if, outside the temperature zone, the wire is
All surfaces shall be flat and opposite surfaces shall be parallel
coupled to cotton thread and the thread is coupled to the
within 0.02 mm.
transducer. If specimen supports of other than the suspension
6. Procedure
type are used, they shall meet the same general specifications.
6.1 Procedure A, Room Temperature Testing—Position the
5. Test Specimens
specimen properly (see Figs. 3 and 4).Activate the equipment
5.1 Preparethespecimenssothattheyareeitherrectangular
so that power adequate to excite the specimen is delivered to
or circular in cross section. Either geometry can be used to
the driving transducer. Set the gain of the detector circuit high
measure both Young’s modulus and shear modulus. However,
enough to detect vibration in the specimen and to display it on
great experimental difficulties in obtaining torsional resonance
the oscilloscope screen with sufficient amplitude to measure
frequencies for a cylindrical specimen usually preclude its use
accurately the frequency at which the signal amplitude is
in determining shear modulus, although the equations for
maximized. Adjust the oscilloscope so that a sharply defined
computing shear modulus with a cylindrical specimen are both
horizontal baseline exists when the specimen is not excited.
simplerandmoreaccuratethanthoseusedwithaprismaticbar.
Scan frequencies with the audio oscillator until specimen
5.2 Resonance frequencies for a given specimen are func-
resonance is indicated by a sinusoidal pattern of maximum
tions of the bar dimensions as well as its density and modulus;
amplitude on the oscilloscope. Find the fundamental mode of
therefore, dimensions should be selected with this relationship
vibrationinflexure,thenfindthefirstovertoneinflexure(Note
3). Establish definitely the fundamental flexural mode by
positioningthedetectorattheappropriatenodalpositionofthe
Smith, R. E., and Hagy, H. E., “A Low Temperature Sonic Resonance
specimen (see Fig. 5). At this point, the amplitude of the
Apparatus for Determining Elastic Properties of Solids,” Internal Report 2195,
Corning Glass Works, April 1961. resonance signal will decrease to zero. The ratio of the first
C848–88 (2006)
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). 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 recommend using only the
fundamental in flexure when computingYoung’s modulus for a rectangu-
larbarbecauseoftheapproximatenatureofPickett’stheory.However,for
the nominal size of bar specified, the values of Young’s modulus
computedusingEq1andEq2willagreewithin1%.Whenthecorrection
factor, T , is greater than 2%, Eq 2 should not be used.
6.2 ProcedureB,ElevatedTemperatureTesting—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 temperature in the
furnace cavity with the furnace doors closed, and so forth, as
FIG. 4 Specimen Positioned for Measurement of Flexural and
will be the case at elevated temperatures. Heat the furnace at a
Torsional Resonance Frequencies Using “Tweeter” Exciter
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 fre-
quencies with time closely to avoid losing the identity of each
frequency. (The overtone in flexure and the 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 also be taken on
cooling; it must be remembered, however, that high tempera-
tures 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), moni-
toring frequencies as the chamber is cooled. Allow the speci-
men to stabilize at minimum temperature for at least 15 min.
Take data on heating. Heating rate should not exceed 50°C/h
and data may be taken at intervals of 10 min or 15°C or as
FIG. 5 Some Modes of Mechanical Vibration in a Bar
desired.
NOTE 4—Precautions should be taken to remove water vapor from the
overtone frequency to the fundamental frequency will be ch
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