ASTM C848-88(2020)

Standard Test Method for Young’s Modulus, Shear Modulus, and Poisson’s Ratio For Ceramic Whitewares 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 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.  
3.2 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.2 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 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. 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 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 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 and determine the applicability of regulatory limitations prior to use.  
1.6 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.

General Information

• Status: Published
• Publication Date: 31-Oct-2020
• ICS: 81.060.20 - Ceramic products
• Technical Committee: C21 - Ceramic Whitewares and Related Products
• Drafting Committee: C21.03 - Methods for Whitewares and Environmental Concerns

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: C848 − 88 (Reapproved 2020)
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 determined for a piece with a particular geometry and density.
Any specimen with a frequency response falling outside this
1.1 This test method covers the determination of the elastic
frequency range is rejected. The actual modulus of each piece
properties of ceramic whiteware materials. Specimens of these
need not be determined as long as the limits of the selected
materials possess specific mechanical resonance frequencies
frequency range are known to include the resonance frequency
which are defined by the elastic moduli, density, and geometry
that the piece must possess if its geometry and density are
of the test specimen. Therefore the elastic properties of a
within specified tolerances.
material can be computed if the geometry, density, and me-
1.5 This standard does not purport to address all of the
chanical resonance frequencies of a suitable test specimen of
safety concerns, if any, associated with its use. It is the
that material can be measured.Young’s modulus is determined
responsibility of the user of this standard to establish appro-
using the resonance frequency in the flexural mode of vibra-
priate safety, health, and environmental practices and deter-
tion.The shear modulus, or modulus of rigidity, is found using
mine the applicability of regulatory limitations prior to use.
torsional resonance vibrations. Young’s modulus and shear
1.6 This international standard was developed in accor-
modulus are used to compute Poisson’s ratio, the factor of
dance with internationally recognized principles on standard-
lateral contraction.
ization established in the Decision on Principles for the
1.2 All ceramic whiteware materials that are elastic,
Development of International Standards, Guides and Recom-
homogeneous,andisotropicmaybetestedbythistestmethod.
mendations issued by the World Trade Organization Technical
This test method is not satisfactory for specimens that have
Barriers to Trade (TBT) Committee.
cracks or voids that represent inhomogeneities in the material;
neither is it satisfactory when these materials cannot be 2. Summary of Test Method
prepared in a suitable geometry.
2.1 This test method measures the resonance frequencies of
NOTE 1—Elastic here means that an application of stress within the test bars of suitable geometry by exciting them at continuously
elastic limit of that material making up the body being stressed will cause
variable frequencies. Mechanical excitation of the specimen is
aninstantaneousanduniformdeformation,whichwillceaseuponremoval
provided through use of a transducer that transforms an initial
ofthestress,withthebodyreturninginstantlytoitsoriginalsizeandshape
electrical signal into a mechanical vibration. Another trans-
withoutanenergyloss.Manyceramicwhitewarematerialsconformtothis
ducer senses the resulting mechanical vibrations of the speci-
definition well enough that this test is meaningful.
NOTE 2—Isotropic means that the elastic properties are the same in all men and transforms them into an electrical signal that can be
directions in the material.
displayed on the screen of an oscilloscope to detect resonance.
Theresonancefrequencies,thedimensions,andthemassofthe
1.3 A cryogenic cabinet and high-temperature furnace are
specimen are used to calculateYoung’s modulus and the shear
described for measuring the elastic moduli as a function of
modulus.
temperature from−195 to 1200°C.
1.4 Modification of the test for use in quality control is
3. Significance and Use
possible. A range of acceptable resonance frequencies is
3.1 This test system has advantages in certain respects over
theuseofstaticloadingsystemsinthemeasurementofceramic
whitewares.
ThistestmethodisunderthejurisdictionofASTMCommitteeC21onCeramic
3.1.1 Only minute stresses are applied to the specimen, thus
Whitewares and Related Productsand is the direct responsibility of Subcommittee
minimizing the possibility of fracture.
C21.03 on Methods for Whitewares and Environmental Concerns.
3.1.2 The period of time during which stress is applied and
Current edition approved Nov. 1, 2020. Published December 2020. Originally
approved in 1976. Last previous edition approved in 2016 as C848–88(2016).
removed is of the order of hundreds of microseconds, making
DOI: 10.1520/C0848-88R20.
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. time scale.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
C848 − 88 (2020)
FIG. 1 Block Diagram of Apparatus
3.2 This test method is suitable for detecting whether a or other similar device, depending on the type of coupling
material meets specifications, if cognizance is given to one chosen for use between the transducer and the specimen. The
important fact: ceramic whiteware materials are sensitive to other transducer, used as a detector, may be a crystal or
thermal history. Therefore, the thermal history of a test magneticreluctancetypeofphonographcartridge.Acapacitive
specimen must be known before the moduli can be considered pickup may be used if desired. The frequency response of the
in terms of specified values. Material specifications should transducer shall be as good as possible with at least a 6.5-kHz
include a 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
provide an accurate frequency determination. A suitable to within 61 Hz.
suspension-coupling system cradles the test specimen, and
4.8 If data at elevated temperatures 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 is capable of controlled heating, frost-free, and
suitable furnace or cryogenic chamber is used. Details of the
uniform in temperature within 65°C over the length of the
equipment are as follows:
specimen at any selected temperature. A suitable cryogenic
4.2 Audio Oscillator, having a continuously variable fre- 3
chamber is shown in Fig. 2.
quency output from about 100 to at least 20 kHz. Frequency
4.10 Any method of specimen suspension shall be used that
drift shall not exceed 1 Hz/min for any given setting.
isadequateforthetemperaturesencounteredintestingandthat
4.3 Audio Amplifier, having a power output sufficient to
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.
C848 − 88 (2020)
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
men sizes are 125 by 15 by 6 mm for bars of rectangular cross
3—Plastic foam
section and 125 by 10 to 12 mm for those of circular cross
4—Vacuum jar
5—Heater disk
section. These specimen sizes should produce a fundamental
6—Copper plate
flexural resonance frequency in the range from 1000 to
7—Thermocouple
2000Hz. Specimens shall have a minimum mass of5gto
8—Sample
9—Suspension wires
avoid coupling effects: any size of specimen that has a suitable
10—Fill port for liquid
length-to-crosssectionratiointermsoffrequencyresponseand
meets the mass minimum may be used. Maximum specimen
FIG. 2 Detail Drawing of Suitable Cryogenic Chamber
size and mass are determined primarily by the test system’s
energy and space capabilities.
shall allow the specimen to vibrate without significant restric-
5.3 Finish specimens using a fine grind, 400 grit or smaller.
tion. Common cotton thread, silica glass fiber thread,
All surfaces shall be flat and opposite surfaces shall be parallel
Nichrome, or platinum wire may be used. If metal wire
within 0.02 mm.
suspension is used in the furnace, coupling characteristics will
be improved if, outside the temperature zone, the wire is
6. Procedure
coupled to cotton thread and the thread is coupled to the
6.1 Procedure A, Room Temperature Testing—Position the
transducer. If specimen supports of other than the suspension
specimen properly (see Figs. 3 and 4).Activate the equipment
type are used, they shall meet the same general specifications.
so that power adequate to excite the specimen is delivered to
the driving transducer. Set the gain of the detector circuit high
5. Test Specimens
enough to detect vibration in the specimen and to display it on
5.1 Preparethespecimenssothattheyareeitherrectangular
the oscilloscope screen with sufficient amplitude to measure
or circular in cross section. Either geometry can be used to
accurately the frequency at which the signal amplitude is
measure both Young’s modulus and shear modulus. However,
maximized. Adjust the oscilloscope so that a sharply defined
great experimental difficulties in obtaining torsional resonance
horizontal baseline exists when the specimen is not excited.
frequencies for a cylindrical specimen usually preclude its use
Scan frequencies with the audio oscillator until specimen
in determining shear modulus, although the equations for
resonance is indicated by a sinusoidal pattern of maximum
computing shear modulus with a cylindrical specimen are both
amplitude on the oscilloscope. Find the fundamental mode of
simplerandmoreaccuratethanthoseusedwithaprismaticbar.
vibrationinflexure,thenfindthefirstovertoneinflexure(Note
5.2 Resonance frequencies for a given specimen are func- 3). Establish definitely the fundamental flexural mode by
tions of the bar dimensions as well as its density and modulus; positioningthedetectorattheappropriatenodalpositionofthe
therefore, dimensions should be selected with this relationship specimen (see Fig. 5). At this point, the amplitude of the
in mind. Make selection of size so that, for anestimated resonance signal will decrease to zero. The ratio of the first
modulus, the resonance frequencies measured will fall within overtone frequency to the fundamental frequency will be
the range of frequency response of the transducers used. approximately 2.70 to 2.75. If a determination of the shear
Representative values of Young’s modulus are 10×10 psi modulusistobemade,offsetthecouplingtothetransducersso
(69GPa) for vitreous triaxial porcelains and 32×10 psi that the torsional mode of vibration may be detected (see Fig.
(220GPa) for 85% alumina porcelains. Recommended speci- 3). Find the fundamental resonance vibration in this mode.
C848 − 88 (2020)
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
thenominalsizeofbarspecified,thevaluesofYoung’smoduluscomputed
usingEq1andEq2willagreewithin1%.Whenthecorrectionfactor, 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 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
FIG. 4 Specimen Positioned for Measurement of Flexural and
frequency. (The overtone in flexure and the fundamental in
Torsional Resonance Frequencies Using “Tweeter” Exciter
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 t
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