ASTM C848-88(1999)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
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Designation:C848 –88(Reapproved 1999)
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 (e) indicates an editorial change since the last revision or reapproval.
1. Scope Any specimen with a frequency response falling outside this
frequency range is rejected. The actual modulus of each piece
1.1 This test method covers the determination of the elastic
need not be determined as long as the limits of the selected
properties of ceramic whiteware materials. Specimens of these
frequency range are known to include the resonance frequency
materials possess specific mechanical resonance frequencies
that the piece must possess if its geometry and density are
which are defined by the elastic moduli, density, and geometry
within specified tolerances.
of the test specimen. Therefore the elastic properties of a
1.5 This standard does not purport to address all of the
material can be computed if the geometry, density, and me-
safety concerns, if any, associated with its use. It is the
chanical resonance frequencies of a suitable test specimen of
responsibility of the user of this standard to establish appro-
that material can be measured.Young’s modulus is determined
priate safety and health practices and determine the applica-
using the resonance frequency in the flexural mode of vibra-
bility of regulatory limitations prior to use.
tion.The shear modulus, or modulus of rigidity, is found using
torsional resonance vibrations. Young’s modulus and shear
2. Summary of Test Method
modulus are used to compute Poisson’s ratio, the factor of
2.1 This test method measures the resonance frequencies of
lateral contraction.
test bars of suitable geometry by exciting them at continuously
1.2 All ceramic whiteware materials that are elastic, homo-
variable frequencies. Mechanical excitation of the specimen is
geneous,andisotropicmaybetestedbythistestmethod. This
provided through use of a transducer that transforms an initial
test method is not satisfactory for specimens that have cracks
electrical signal into a mechanical vibration. Another trans-
or voids that represent inhomogeneities in the material; neither
ducer senses the resulting mechanical vibrations of the speci-
is it satisfactory when these materials cannot be prepared in a
men and transforms them into an electrical signal that can be
suitable geometry.
displayed on the screen of an oscilloscope to detect resonance.
NOTE 1—Elastic here means that an application of stress within the
Theresonancefrequencies,thedimensions,andthemassofthe
elastic limit of that material making up the body being stressed will cause
specimen are used to calculateYoung’s modulus and the shear
aninstantaneousanduniformdeformation,whichwillceaseuponremoval
modulus.
ofthestress,withthebodyreturninginstantlytoitsoriginalsizeandshape
withoutanenergyloss.Manyceramicwhitewarematerialsconformtothis
3. Significance and Use
definition well enough that this test is meaningful.
NOTE 2—Isotropic means that the elastic properties are the same in all 3.1 This test system has advantages in certain respects over
directions in the material.
theuseofstaticloadingsystemsinthemeasurementofceramic
whitewares.
1.3 A cryogenic cabinet and high-temperature furnace are
3.1.1 Only minute stresses are applied to the specimen, thus
described for measuring the elastic moduli as a function of
minimizing the possibility of fracture.
temperature from−195 to 1200°C.
3.1.2 The period of time during which stress is applied and
1.4 Modification of the test for use in quality control is
removed is of the order of hundreds of microseconds, making
possible. A range of acceptable resonance frequencies is
it feasible to perform measurements at temperatures where
determined for a piece with a particular geometry and density.
delayed elastic and creep effects proceed on a much-shortened
time scale.
This test method is under the jurisdiction of ASTM Committee C-21 on
3.2 This test method is suitable for detecting whether a
Ceramic Whitewares and Related Products and is the direct responsibility of
material meets specifications, if cognizance is given to one
Subcommittee C21.03 on Test Methods for Whiteware Properties.
important fact: ceramic whiteware materials are sensitive to
Current edition approved Sept. 30, 1988. Published November 1988. Originally
thermal history. Therefore, the thermal history of a test
published as C848–76. Last previous edition C848–88 (1994).
Spinner, S., and Tefft, W. E., “A Method for Determining Mechanical
specimen must be known before the moduli can be considered
Resonance Frequencies and for Calculating Elastic Moduli from These Frequen-
cies,” Proceedings, ASTM, 1961, pp. 1221–1238.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
C848 –88 (1999)
in terms of specified values. Material specifications should 4.5 Power Amplifier, in the detector circuit shall be imped-
include a specific thermal treatment for all test specimens. ance matched with the type of detector transducer selected and
shall serve as a prescope amplifier.
4. Apparatus
4.6 Cathode-Ray Oscilloscope, shall be any model suitable
4.1 The test apparatus is shown in Fig. 1. It consists of a
for general laboratory work.
variable-frequency audio oscillator, used to generate a sinusoi-
4.7 Frequency Counter, shall be able to measure frequen-
dal voltage, and a power amplifier and suitable transducer to
cies to within 61 Hz.
convert the electrical signal to a mechanical driving vibration.
4.8 If data at elevated temperatures are desired, a furnace
A frequency meter monitors the audio oscillator output to
shall be used that is capable of controlled heating and cooling.
provide an accurate frequency determination. A suitable
It shall have a specimen zone 180 mm in length, which will be
suspension-coupling system cradles the test specimen, and
uniform in temperature within 65°C throughout the range of
another transducer acts to detect mechanical resonance in the
specimen and to convert it into an electrical signal which is temperatures encountered in testing.
passedthroughanamplifieranddisplayedontheverticalplates
4.9 For data at cryogenic temperatures, any chamber shall
ofanoscilloscope.IfaLissajousfigureisdesired,theoutputof
suffice that is capable of controlled heating, frost-free, and
the oscillator is also coupled to the horizontal plates of the
uniform in temperature within 65°C over the length of the
oscilloscope. If temperature-dependent data are desired, a
specimen at any selected temperature. A suitable cryogenic
suitable furnace or cryogenic chamber is used. Details of the
chamber is shown in Fig. 2.
equipment are as follows:
4.10 Any method of specimen suspension shall be used that
4.2 Audio Oscillator, having a continuously variable fre-
isadequateforthetemperaturesencounteredintestingandthat
quency output from about 100 to at least 20 kHz. Frequency
shall allow the specimen to vibrate without significant restric-
drift shall not exceed 1 Hz/min for any given setting.
tion. Common cotton thread, silica glass fiber thread,
4.3 Audio Amplifier, having a power output sufficient to
Nichrome, or platinum wire may be used. If metal wire
ensurethatthetypeoftransducerusedcanexciteanyspecimen
suspension is used in the furnace, coupling characteristics will
the mass of which falls within a specified range.
be improved if, outside the temperature zone, the wire is
4.4 Transducers—Two are required; one used as a driver
coupled to cotton thread and the thread is coupled to the
maybeaspeakerofthetweetertypeoramagneticcuttinghead
transducer. If specimen supports of other than the suspension
or other similar device, depending on the type of coupling
type are used, they shall meet the same general specifications.
chosen for use between the transducer and the specimen. The
other transducer, used as a detector, may be a crystal or
magneticreluctancetypeofphonographcartridge.Acapacitive
pickup may be used if desired. The frequency response of the
Smith, R. E., and Hagy, H. E., “A Low Temperature Sonic Resonance
transducer shall be as good as possible with at least a 6.5-kHz
Apparatus for Determining Elastic Properties of Solids,” Internal Report 2195,
bandwidth before 3-dB power loss occurs. Corning Glass Works, April 1961.
FIG. 1 Block Diagram of Apparatus
C848 –88 (1999)
5.3 Finish specimens 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
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
vibrationinflexure,thenfindthefirstovertoneinflexure(Note
3). Establish definitely the fundamental flexural mode by
positioningthedetectorattheappropriatenodalpositionofthe
1—Cylindrical glass jar
specimen (see Fig. 5). At this point, the amplitude of the
2—Glass wool
resonance signal will decrease to zero. The ratio of the first
3—Plastic foam
4—Vacuum jar
overtone frequency to the fundamental frequency will be
5—Heater disk
approximately 2.70 to 2.75. If a determination of the shear
6—Copper plate
modulusistobemade,offsetthecouplingtothetransducersso
7—Thermocouple
8—Sample
that the torsional mode of vibration may be detected (see Fig.
9—Suspension wires
3). Find the fundamental resonance vibration in this mode.
10—Fill port for liquid
Identify the torsional mode by centering the detector with
FIG. 2 Detail Drawing of Suitable Cryogenic Chamber
respect to the width of the specimen and observing that the
amplitude of the resonance signal decreases to zero; if it does
not,thesignalisanovertoneofflexureoraspuriousfrequency
5. Test Specimens
generated elsewhere in the system. Dimensions and weight of
5.1 Preparethespecimenssothattheyareeitherrectangular
the specimen may be measured before or after the test.
or circular in cross section. Either geometry can be used to
Measure the dimensions with a micrometer caliper capable of
measure both Young’s modulus and shear modulus. However,
an accuracy of 60.01 mm; measure the weight with a balance
great experimental difficulties in obtaining torsional resonance
capable of 610-g accuracy.
frequencies for a cylindrical specimen usually preclude its use
NOTE 3—It is recommended that the first overtone in flexure be
in determining shear modulus, although the equations for
computing shear modulus with a cylindrical specimen are both
simplerandmoreaccuratethanthoseusedwithaprismaticbar.
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. Make selection of size so that, for anestimated
modulus, the resonance frequencies measured will fall within
the range of frequency response of the transducers used.
Representative values of Young’s modulus are 10 310 psi
(69 GPa) for vitreous triaxial porcelains and 32 310 psi (220
GPa) for 85% alumina porcelains. Recommended specimen
sizes are 125 by 15 by 6 mm for bars of rectangular cross
section and 125 by 10 to 12 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 of5gto avoid
coupling effects: any size of specimen that has a suitable
length-to-crosssectionratiointermsoffrequencyresponseand
meets the mass minimum may be used. Maximum specimen
FIG. 3 Specimen Positioned for Measurement of Flexural and
size and mass are determined primarily by the test system’s
Torsional Resonance Frequencies Using Thread or Wire
energy and space capabilities. Suspension
C848 –88 (1999)
Determine the resonant frequencies at room temperature 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 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
FIG. 4 Specimen Positioned for Measurement of Flexural and
Torsional Resonance Frequencies Using “Tweeter” Exciter 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
desired.
NOTE 4—Precautions should be taken to remove water vapor from the
chamber by flushing with dry nitrogen gas before chilling so that frost
deposits on the specimen do not cause anomalous results.
7. Calculation
7.1 Young’s Modulus:
7.1.1 For the fundamental in flexure of a rectangular bar
(Note 5):
3 3 2 –8
E 596.517 ~L /bt ! Twf 310 (1)
where:
E = Young’s modulus, kgf/cm ;
L = length of the bar, cm;
b = width of the bar, cm;
FIG. 5 Some Modes of Mech
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