ASTM C1198-20

Standard Test Method for Dynamic Young’s Modulus, Shear Modulus, and Poisson’s Ratio for Advanced Ceramics by Sonic Resonance

SIGNIFICANCE AND USE
5.1 This test method may be used for material development, characterization, design data generation, and quality control purposes. It is specifically appropriate for determining the modulus of advanced ceramics that are elastic, homogeneous, and isotropic.  
5.1.1 This test method is nondestructive in nature. Only minute stresses are applied to the specimen, thus minimizing the possibility of fracture.  
5.1.2 The period of time during which measurement stress is applied and removed is of the order of hundreds of microseconds. With this test method it is feasible to perform measurements at high temperatures, where delayed elastic and creep effects would invalidate modulus measurements calculated from static loading.  
5.2 This test method has advantages in certain respects over the use of static loading systems for measuring moduli in advanced ceramics. It is nondestructive in nature and can be used for specimens prepared for other tests. Specimens are subjected to minute strains; hence, the moduli are measured at or near the origin of the stress-strain curve with the minimum possibility of fracture. The period of time during which measurement stress is applied and removed is of the order of hundreds of microseconds. With this test method it is feasible to perform measurements at high temperatures, where delayed elastic and creep effects would invalidate modulus measurements calculated from static loading.  
5.3 The sonic resonant frequency technique can also be used as a nondestructive evaluation tool for detecting and screening defects (cracks, voids, porosity, density variations) in ceramic parts. These defects may change the elastic response and the observed resonant frequency of the test specimen. Guide E2001 describes a procedure for detecting such defects in metallic and nonmetallic parts using the resonant frequency method.  
5.4 Modification of this test method for use in quality control is possible. A range of acceptable resonant frequencies is determ...
SCOPE
1.1 This test method covers the determination of the dynamic elastic properties of advanced ceramics. Specimens of these materials possess specific mechanical resonant frequencies that are determined by the elastic modulus, mass, and geometry of the test specimen. Therefore, the dynamic elastic properties of a material can be computed if the geometry, mass, and mechanical resonant frequencies of a suitable rectangular or cylindrical test specimen of that material can be measured. The resonant frequencies in flexure and torsion are measured by mechanical excitation of vibrations of the test specimen in a suspended mode (Section 4 and Figs. 1 and 4). Dynamic Young’s modulus is determined using the resonant frequency in the flexural mode of vibration. The dynamic shear modulus, or modulus of rigidity, is found using torsional resonant vibrations. Dynamic Young’s modulus and dynamic shear modulus are used to compute Poisson’s ratio.  
1.2 This test method is specifically appropriate for advanced ceramics that are elastic, homogeneous, and isotropic  (1).2 Advanced ceramics of a composite character (particulate, whisker, or fiber reinforced) may be tested by this test method with the understanding that the character (volume fraction, size, morphology, distribution, orientation, elastic properties, and interfacial bonding) of the reinforcement in the test specimen will have a direct effect on the elastic properties. These reinforcement effects must be considered in interpreting the test results for composites. This test method is not satisfactory for specimens that have cracks or voids that are major discontinuities in the specimen. Neither is the test method satisfactory when these materials cannot be fabricated in a uniform rectangular or circular cross-section.  
1.3 A high-temperature furnace and cryogenic cabinet are described for measuring the dynamic elastic moduli as a function of temperature from −195 to 1200 °C.  
...

General Information

• Status: Published
• Publication Date: 31-Dec-2019
• ICS: 81.060.30 - Advanced ceramics
• Technical Committee: C28 - Advanced Ceramics
• Drafting Committee: C28.01 - Mechanical Properties and Performance

Relations

• Replaces: ASTM C1198-09(2013) - Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio for Advanced Ceramics by Sonic Resonance
• Effective Date: 01-Jan-2020
• Refers: ASTM C747-23 - Standard Test Method for Moduli of Elasticity and Fundamental Frequencies of Carbon and Graphite Materials by Sonic Resonance
• Effective Date: 01-Oct-2023
• Refers: ASTM C1145-19 - Standard Terminology of Advanced Ceramics
• Effective Date: 01-Jul-2019
• Refers: ASTM E2001-18 - Standard Guide for Resonant Ultrasound Spectroscopy for Defect Detection in Both Metallic and Non-metallic Parts
• Effective Date: 01-Nov-2018
• Refers: ASTM C747-16 - Standard Test Method for Moduli of Elasticity and Fundamental Frequencies of Carbon and Graphite Materials by Sonic Resonance
• Effective Date: 01-Oct-2016
• Refers: ASTM C215-14 - Standard Test Method for Fundamental Transverse, Longitudinal, and<brk/> Torsional Resonant Frequencies of Concrete Specimens
• Effective Date: 15-Dec-2014
• Refers: ASTM C1259-14 - Standard Test Method for Dynamic Young&rsquo;s Modulus, Shear Modulus, and Poisson&rsquo;s Ratio for Advanced Ceramics by Impulse Excitation of Vibration
• Effective Date: 01-Jan-2014
• Refers: ASTM E2001-13 - Standard Guide for Resonant Ultrasound Spectroscopy for Defect Detection in Both Metallic and Non-metallic Parts
• Effective Date: 01-Dec-2013
• Refers: ASTM E1875-13 - Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Sonic Resonance
• Effective Date: 01-Nov-2013
• Refers: ASTM C1161-13 - Standard Test Method for Flexural Strength of Advanced Ceramics at Ambient Temperature
• Effective Date: 01-Aug-2013
• Refers: ASTM C1145-06(2013)e1 - Standard Terminology of Advanced Ceramics
• Effective Date: 01-Feb-2013
• Refers: ASTM C1145-06(2013) - Standard Terminology of Advanced Ceramics
• Effective Date: 01-Feb-2013
• Refers: ASTM C372-94(2012) - Standard Test Method for Linear Thermal Expansion of Porcelain Enamel and Glaze Frits and Fired Ceramic Whiteware Products by the Dilatometer Method
• Effective Date: 01-Apr-2012
• Refers: ASTM C848-88(2011) - Standard Test Method for Young's Modulus, Shear Modulus, and Poisson's Ratio For Ceramic Whitewares by Resonance
• Effective Date: 01-Mar-2011
• Refers: ASTM C747-93(2010)e1 - Standard Test Method for Moduli of Elasticity and Fundamental Frequencies of Carbon and Graphite Materials by Sonic Resonance
• Effective Date: 01-May-2010

Overview

ASTM C1198-20 is a globally recognized standard test method for determining the dynamic Young’s modulus, shear modulus, and Poisson’s ratio of advanced ceramics using sonic resonance. This nondestructive test evaluates the elastic properties of advanced ceramics by measuring their mechanical resonant frequencies, which depend on a specimen’s mass, geometry, and modulus. The technique is valuable for material development, characterization, design validation, and quality control within industries that use high-performance ceramic materials.

Key Topics

• Dynamic Elastic Properties: The test determines key properties such as dynamic Young’s modulus and dynamic shear modulus, critical for predicting material behavior under operational conditions.
• Sonic Resonance Technique: Specimens are mechanically excited at variable frequencies to find their natural resonant frequencies in both flexural and torsional modes, allowing precise calculation of elastic moduli.
• Nondestructive Evaluation: By applying only minimal stress for a very short duration (hundreds of microseconds), the test avoids damaging the specimen, making it suitable for high-value or limited-quantity ceramic materials.
• High and Low Temperature Testing: Measurements can be performed from cryogenic temperatures (down to −195°C) up to elevated temperatures (up to 1200°C), supporting wide-ranging applications and research into temperature-dependent behavior.
• Defect Detection: Changes in resonant frequency can indicate internal defects, such as cracks, voids, porosity, or density variations, making the method useful for screening and quality assurance.

Applications

ASTM C1198-20 is widely used across industries where advanced ceramics are integral, including electronics, aerospace, automotive, energy, and medical technologies. Typical applications include:

• Material Characterization: Assessing material properties to support research, product development, and validation of ceramic components.
• Quality Control: Rapid, nondestructive evaluation of production batches to ensure compliance with mechanical strength and integrity requirements.
• Design Data Generation: Providing reliable modulus values for engineering calculations and modeling of ceramic parts in service.
• High-Temperature and Cryogenic Applications: Ensuring ceramic components maintain performance standards under extreme operating conditions.
• Defect Screening: Quickly identifying nonconforming or defective products before further processing or deployment.

Related Standards

ASTM C1198-20 references and complements multiple other standards for mechanical testing and resonance evaluation, including:

• ASTM C215 - Fundamental resonant frequencies of concrete specimens
• ASTM C623 - Young’s modulus, shear modulus, and Poisson’s ratio for glass and glass-ceramics by resonance
• ASTM C747 - Moduli of elasticity and fundamental frequencies for carbon and graphite materials
• ASTM C848 - Moduli for ceramic whitewares by resonance
• ASTM C1161 - Flexural strength of advanced ceramics at ambient temperature
• ASTM C1259 - Dynamic properties of advanced ceramics by impulse excitation of vibration
• ASTM E1876 - Dynamic modulus by impulse excitation of vibration
• ASTM E2001 - Resonant ultrasound for defect detection in metallic and non-metallic parts
• ISO 14704 - Flexural strength of monolithic ceramics at room temperature

Practical Value

ASTM C1198-20 provides a robust framework for accurately and efficiently determining the elastic properties of advanced ceramics, supporting critical decision-making throughout material development, product qualification, and quality assurance processes. Its nondestructive nature preserves specimen integrity and enables integration with other mechanical tests or subsequent material use. The method’s sensitivity to defects further enhances production reliability and lifetime prediction for ceramic components in demanding environments.

For organizations involved in the manufacture, development, or application of advanced ceramics, compliance with ASTM C1198-20 ensures alignment with international mechanical property testing best practices, supporting competitive quality and safety standards.

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: C1198 − 20
Standard Test Method for
Dynamic Young’s Modulus, Shear Modulus, and Poisson’s
Ratio for Advanced Ceramics by Sonic Resonance
This standard is issued under the fixed designation C1198; 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 There are material-specific ASTM standards that cover
the determination of resonance frequencies and elastic proper-
1.1 This test method covers the determination of the dy-
ties of specific materials by sonic resonance or by impulse
namic elastic properties of advanced ceramics. Specimens of
excitationofvibration.TestMethodsC215,C623,C747,C848,
these materials possess specific mechanical resonant frequen-
C1259, E1875, and E1876 may differ from this test method in
cies that are determined by the elastic modulus, mass, and
several areas (for example: sample size, dimensional
geometry of the test specimen. Therefore, the dynamic elastic
tolerances, sample preparation, calculation details, etc.). The
propertiesofamaterialcanbecomputedifthegeometry,mass,
testing of those materials should be done in compliance with
and mechanical resonant frequencies of a suitable rectangular
theappropriatematerial-specificstandards.Wherepossible,the
or cylindrical test specimen of that material can be measured.
procedures, sample specifications, and calculations in this
The resonant frequencies in flexure and torsion are measured
standard are consistent with the other test methods.
by mechanical excitation of vibrations of the test specimen in
a suspended mode (Section 4 and Figs. 1 and 4). Dynamic 1.5 The values stated in SI units are to be regarded as the
Young’s modulus is determined using the resonant frequency standard. The non-SI values given in parentheses are for
in the flexural mode of vibration.The dynamic shear modulus, information only and are not considered standard.
or modulus of rigidity, is found using torsional resonant
1.6 This standard does not purport to address all of the
vibrations. Dynamic Young’s modulus and dynamic shear
safety concerns, if any, associated with its use. It is the
modulus are used to compute Poisson’s ratio.
responsibility of the user of this standard to establish appro-
priate safety, health, and environmental practices and deter-
1.2 Thistestmethodisspecificallyappropriateforadvanced
mine the applicability of regulatory limitations prior to use.
ceramics that are elastic, homogeneous, and isotropic (1).
1.7 This international standard was developed in accor-
Advanced ceramics of a composite character (particulate,
dance with internationally recognized principles on standard-
whisker, or fiber reinforced) may be tested by this test method
ization established in the Decision on Principles for the
with the understanding that the character (volume fraction,
Development of International Standards, Guides and Recom-
size, morphology, distribution, orientation, elastic properties,
mendations issued by the World Trade Organization Technical
and interfacial bonding) of the reinforcement in the test
Barriers to Trade (TBT) Committee.
specimen will have a direct effect on the elastic properties.
These reinforcement effects must be considered in interpreting
2. Referenced Documents
the test results for composites. This test method is not
satisfactory for specimens that have cracks or voids that are
2.1 ASTM Standards:
major discontinuities in the specimen. Neither is the test
C215 Test Method for Fundamental Transverse,
method satisfactory when these materials cannot be fabricated
Longitudinal, and Torsional Resonant Frequencies of
in a uniform rectangular or circular cross-section.
Concrete Specimens
C372Test Method for Linear Thermal Expansion of Porce-
1.3 A high-temperature furnace and cryogenic cabinet are
lainEnamelandGlazeFritsandFiredCeramicWhiteware
described for measuring the dynamic elastic moduli as a
Products by the Dilatometer Method
function of temperature from −195 to 1200°C.
C623Test Method for Young’s Modulus, Shear Modulus,
and Poisson’s Ratio for Glass and Glass-Ceramics by
This test method is under the jurisdiction of ASTM Committee C28 on
Resonance
Advanced Ceramics and is the direct responsibility of Subcommittee C28.01 on
Mechanical Properties and Performance.
Current edition approved Jan. 1, 2020. Published January 2020. Originally
approved in 1991. Last previous edition approved in 2013 as C1198– 09 (2013). For referenced ASTM standards, visit the ASTM website, www.astm.org, or
DOI: 10.1520/C1198-20. contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
The boldface numbers given in parentheses refer to a list of references at the Standards volume information, refer to the standard’s Document Summary page on
end of the text. the ASTM website.
*A Summary of Changes section appears at the end of this standard
Copyright ©ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA19428-2959. United States
C1198 − 20
−2
C747TestMethodforModuliofElasticityandFundamental 3.1.8 shear modulus (G) [FL ],n—the elastic modulus in
Frequencies of Carbon and Graphite Materials by Sonic shear or torsion. Also called modulus of rigidity or torsional
Resonance modulus. E6
C848Test Method for Young’s Modulus, Shear Modulus, −2
3.1.9 Young’s modulus(E)[FL ],n—theelasticmodulusin
and Poisson’s Ratio For Ceramic Whitewares by Reso-
tension or compression. E6
nance
3.2 Definitions of Terms Specific to This Standard:
C1145Terminology of Advanced Ceramics
3.2.1 anti-nodes, n—an unconstrained slender rod or bar in
C1161Test Method for Flexural Strength of Advanced
resonance contains two or more locations that have local
Ceramics at Ambient Temperature
maximumdisplacements,calledanti-nodes.Forthefundamen-
C1259Test Method for Dynamic Young’s Modulus, Shear
talflexureresonance,theanti-nodesarelocatedatthetwoends
Modulus, and Poisson’s Ratio forAdvanced Ceramics by
and the center of the specimen.
Impulse Excitation of Vibration
E6Terminology Relating to Methods of Mechanical Testing
3.2.2 elastic, adj—the property of a material such that an
E1875Test Method for Dynamic Young’s Modulus, Shear
application of stress within the elastic limit of that material
Modulus, and Poisson’s Ratio by Sonic Resonance
making up the body being stressed will cause an instantaneous
E1876Test Method for Dynamic Young’s Modulus, Shear
anduniformdeformation,thatwillbeeliminateduponremoval
Modulus, and Poisson’s Ratio by Impulse Excitation of
of the stress, with the body returning instantly to its original
Vibration
size and shape without energy loss. Most advanced ceramics
E2001Guide for Resonant Ultrasound Spectroscopy for
conform to this definition well enough to make this resonance
Defect Detection in Both Metallic and Non-metallic Parts
test valid.
2.2 ISO Standard:
3.2.3 flexural vibrations, n—the vibrations that occur when
ISO 14704Test Method for Flexural Strength of Monolithic
the oscillations in a slender rod or bar are in the plane normal
Ceramics at Room Temperature
to the length dimension.
3. Terminology
3.2.4 homogeneous, adj—the condition of a specimen such
that the composition and density are uniform, such that any
3.1 Definitions:
smaller specimen taken from the original is representative of
3.1.1 advanced ceramic, n—a highly engineered, high
thewhole.Practically,aslongasthegeometricaldimensionsof
performance, predominately nonmetallic, inorganic, ceramic
thetestspecimenarelargewithrespecttothesizeofindividual
material having specific functional attributes. C1145
grains, crystals, or components, the body can be considered
3.1.2 dynamic elastic modulus, n—the elastic modulus,
homogeneous.
either Young’s modulus or shear modulus, that is measured in
a dynamic mechanical measurement. E1876 3.2.5 isotropic, adj—the condition of a specimen such that
thevaluesoftheelasticpropertiesarethesameinalldirections
3.1.3 dynamic mechanical measurement, n—a technique in
in the material.Advanced ceramics are considered isotropic on
which either the modulus or damping, or both, of a substance
a macroscopic scale, if they are homogeneous and there is a
under oscillatory load or displacement is measured as a
random distribution and orientation of phases, crystallites, and
function of temperature, frequency, or time, or combination
components.
thereof. E6
−2
3.2.6 nodes, n—a slender rod or bar in resonance contains
3.1.4 elastic limit [FL ],n—the greatest stress that a
one or more locations having a constant zero displacement,
material is capable of sustaining without permanent strain
callednodes.Forthefundamentalflexuralresonance,thenodes
remaining upon complete release of the stress. E6
are located at 0.224 L from each end, where L is the length of
−2
3.1.5 elastic modulus [FL ],n—the ratio of stress to strain
the specimen.
below the proportional limit.
3.2.7 resonance, n—a slender rod or bar driven into one of
3.1.6 Poisson’s ratio (µ) [nd],n—the absolute value of the
the modes of vibration described in 3.2.3 or 3.2.9 is said to be
ratio of transverse strain to the corresponding axial strain
in resonance when the imposed frequency is such that the
resulting from uniformly distributed axial stress below the
resultantdisplacementsforagivenamountofdrivingforceare
proportional limit of the material. E6
at a maximum. The resonant frequencies are natural vibration
3.1.6.1 Discussion—In isotropic materialsYoung’s modulus
frequencies that are determined by the elastic modulus, mass,
(E), shear modulus (G), and Poisson’s ratio (µ) are related by
and dimensions of the test specimen.
the following equation:
3.2.8 slender rod or bar, n—in dynamic elastic property
µ 5 ~E/2G! 2 1
testing, a specimen whose ratio of length to minimum cross-
−2
3.1.7 proportional limit [FL ],n—the greatest stress that a
sectional dimension is at least five and preferably in the range
material is capable of sustaining without deviation from
of 20 to 25.
proportionality of stress to strain (Hooke’s law). E6
3.2.9 torsional vibrations, n—thevibrationsthatoccurwhen
theoscillationsineachcross-sectionalplaneofaslenderrodor
Available from International Organization for Standardization (ISO), ISO
bar are such that the plane twists around the length dimension
Central Secretariat, BIBC II, Chemin de Blandonnet 8, CP 401, 1214 Vernier,
Geneva, Switzerland, http://www.iso.org. axis.
C1198 − 20
4. Summary of Test Method frequency that the specimen must possess if its geometry and
mass are within specified tolerances.
4.1 This test method measures the resonant frequencies of
test specimens of suitable geometry by exciting them at
6. Interferences
continuously variable frequencies. Mechanical excitation of
6.1 The relationships between resonant frequency and dy-
the bars is provided through the use of a transducer that
namic modulus presented herein are specifically applicable to
transforms a cyclic electrical signal into a cyclic mechanical
homogeneous, elastic, isotropic materials.
forceonthespecimen.Asecondtransducersensestheresulting
6.1.1 This test method of determining the moduli is appli-
mechanical vibrations of the specimen and transforms them
cable to composite ceramics and inhomogeneous materials
into an electrical signal. The amplitude and frequency of the
onlywithcarefulconsiderationoftheeffectofinhomogeneities
signalaremeasuredbyanoscilloscopeorothermeanstodetect
and anisotropy. The character (volume fraction, size,
resonance. The resonant frequencies, dimensions, and mass of
morphology, distribution, orientation, elastic properties, and
the specimen are used to calculate dynamic Young’s modulus
interfacial bonding) of the reinforcement/inhomogeneities in
and dynamic shear modulus.
the specimens will have a direct effect on the elastic properties
of the specimen as a whole. These effects must be considered
5. Significance and Use
in interpreting the test results for composites and inhomoge-
5.1 Thistestmethodmaybeusedformaterialdevelopment,
neous materials.
characterization, design data generation, and quality control
6.1.2 If specific surface treatments (coatings, machining,
purposes. It is specifically appropriate for determining the
grinding, etching, etc.) change the elastic properties of the
modulus of advanced ceramics that are elastic, homogeneous,
near-surface material, there will be accentuated effects on the
and isotropic.
properties measured by this flexural method, as compared to
5.1.1 This test method is nondestructive in nature. Only
static/bulk measurements by tensile or compression testing.
minute stresses are applied to the specimen, thus minimizing
6.1.3 This test method is not satisfactory for specimens that
the possibility of fracture.
have major discontinuities, such as large cracks (internal or
surface) or voids.
5.1.2 The period of time during which measurement stress
is applied and removed is of the order of hundreds of
6.2 This test method for determining moduli is limited to
microseconds. With this test method it is feasible to perform
specimens with regular geometries (rectangular parallelepiped
measurements at high temperatures, where delayed elastic and
and cylinders) for which analytical equations are available to
creep effects would invalidate modulus measurements calcu-
relate geometry, mass, and modulus to the resonant vibration
lated from static loading.
frequencies. This test method is not appropriate for determin-
ing the elastic properties of materials which cannot be fabri-
5.2 This test method has advantages in certain respects over
cated into such geometries.
the use of static loading systems for measuring moduli in
6.2.1 The analytical equations assume parallel/concentric
advanced ceramics. It is nondestructive in nature and can be
dimensions for the regular geometries of the specimen. Devia-
used for specimens prepared for other tests. Specimens are
tions from the specified tolerances for the dimensions of the
subjected to minute strains; hence, the moduli are measured at
specimens will change the resonant frequencies and introduce
or near the origin of the stress-strain curve with the minimum
error into the calculations.
possibility of fracture. The period of time during which
6.2.2 Edge treatments such as chamfers or radii are not
measurement stress is applied and removed is of the order of
considered in the analytical equations. Edge chamfers on
hundreds of microseconds. With this test method it is feasible
flexure bars prepared according to Test Method C1161 will
to perform measurements at high temperatures, where delayed
change the resonant frequency of the test bars and introduce
elastic and creep effects would invalidate modulus measure-
error into the calculations of the dynamic modulus. It is
ments calculated from static loading.
recommended that specimens for this test not have chamfered
5.3 Thesonicresonantfrequencytechniquecanalsobeused
or rounded edges.Alternately, if narrow rectangular specimens
as a nondestructive evaluation tool for detecting and screening
with chamfers or edge radii are tested, then the procedures in
defects (cracks, voids, porosity, density variations) in ceramic
Annex A1 should be used to correct the calculated Young’s
parts. These defects may change the elastic response and the
modulus, E.
observed resonant frequency of the test specimen. Guide
6.2.3 For specimens with as-fabricated/rough or uneven
E2001 describes a procedure for detecting such defects in
surfaces, variations in dimension can have a significant effect
metallic and nonmetallic parts using the resonant frequency
in the calculations. For example, in the calculation of the
method.
dynamic modulus, the modulus value is inversely proportional
tothecubeofthethickness.Uniformspecimendimensionsand
5.4 Modification of this test method for use in quality
precise measurements are essential for accurate results.
control is possible.Arange of acceptable resonant frequencies
is determined for a specimen with a particular geometry and
7. Apparatus
mass.Any specimen with a frequency response falling outside
this frequency range is rejected. The actual modulus of each 7.1 The test apparatus is shown in Fig. 1. It consists of a
specimen need not be determined as long as the limits of the variable-frequency audio oscillator, used to generate a sinusoi-
selected frequency range are known to include the resonant dal voltage, and a power amplifier and suitable transducer to
C1198 − 20
7.7 Frequency Counter, preferably digital, shall be able to
measure frequencies to within 61 Hz.
7.8 Furnace—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 large enough for the
specimen to be uniform in temperature within 65°C along its
length through the range of temperatures encountered in
testing. It is recommended that an independent thermocouple
be placed in close proximity to (within 5 mm), but not
touching, the center of the specimen to accurately measure
temperature during heating and cooling.
7.9 Cryogenic Chamber—For data at cryogenic
temperatures,anychambershallsufficethatshallbecapableof
controlled heating/cooling, frost-free, and uniform in tempera-
ture within 65°C over the length of the specimen at any
FIG. 1 Block Diagram of a Typical Test Apparatus
selectedtemperature.Asuitablecryogenicchamberisshownin
Fig. 2 (2). It is recommended that an independent thermo-
couple be placed in close proximity to (within 5 mm), but not
convert the electrical signal to a mechanical driving vibration.
touching, the center of the specimen to accurately measure
A frequency meter (preferably digital) monitors the audio
temperature during heating and cooling.
oscillator output to provide an accurate frequency determina-
7.10 Specimen Suspension—Any method of specimen sus-
tion. A suitable suspension-coupling system supports the test
pension shall be used that is adequate for the temperatures
specimen.Another transducer acts to detect mechanical vibra-
tion in the specimen and to convert it into an electrical signal encountered in testing and that allows the specimen to vibrate
without significant restriction.Thread suspension is the system
that is passed through an amplifier and displayed on an
indicating meter. The meter may be a voltmeter, ofchoiceforcryogenicandhigh-temperaturetesting.(SeeFig.
1 and Fig. 3.) Common cotton thread, silica-glass fiber thread,
microammeter, or oscilloscope. An oscilloscope is recom-
mended because it enables the operator to positively identify oxidation-resistant nickel (or platinum) alloy wire, or platinum
wire may be used. If metal wire suspension is used in the
resonances, including higher-order harmonics, by Lissajous
figureanalysis.IfaLissajousfigureisdesired,theoutputofthe furnace, coupling characteristics will be improved if, outside
the temperature zone, the wire is coupled to cotton thread, and
oscillator is also coupled to the horizontal plates of the
oscilloscope. If temperature-dependent data are desired, a thethreadiscoupledtothetransducer.Thespecimenshouldbe
initially suspended at distances of approximately 0.1 L from
suitable furnace or cryogenic chamber is used. Details of the
equipment are as follows: each end. The specimen should not be suspended at its
7.2 Audio Oscillator, having a continuously variable fre-
quencyoutputfromabout100Hztoatleast30kHz.Frequency
drift shall not exceed 1 Hz/min for any given setting.
7.3 Audio Amplifier, having a power output sufficient to
ensurethatthetypeoftransducerusedcanexciteanyspecimen
the mass of which falls within a specified range.
7.4 Transducers—Two are required; one used as a driver
maybeaspeakerofthetweetertypeoramagneticcuttinghead
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 photograph cartridge.Acapacitive
pickup may be used if desired. An electromagnetic coupling
system with an attached metal foil may also be used, with due
consideration for effects of the foil on the natural vibration of
1—Cylindrical glass jar
the test bar. The frequency response of the transducer across
2—Glass wool
3—Plastic foam
the frequency range of interest shall have at least a 6.5-kHz
4—Vacuum jar
bandwidth before −3 dB power loss occurs.
5—Heater disk
6—Copper plate
7.5 Power Amplifier, in the detector circuit shall be imped-
7—Thermocouple
ance matched with the type of detector transducer selected and
8—Sample
shall serve as a prescope amplifier.
9—Suspension wires
10—Fill port for liquid
7.6 Cathode-Ray Oscilloscope, any model suitable for gen-
eral laboratory work. FIG. 2 Detailed Drawing of a Typical Cryogenic Chamber
C1198 − 20
sional resonant 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 rectangular bar.
8.2 Resonantfrequenciesforagivenspecimenarefunctions
ofthebardimensionsaswellasitsmassandmoduli;therefore,
dimensions should be selected with this relationship in mind.
Make selection of size so that, for an estimated modulus, the
resonant frequencies measured will fall within the range of
frequency response of the transducers used.Aslender rod with
aratiooflengthtominimumcross-sectionaldimensiongreater
than ten and approximately 25 is preferred for ease in calcu-
lation. For shear modulus measurements of rectangular bars, a
ratio of width to thickness of five is recommended for
minimizing experimental difficulties. Suitable rectangular
FIG. 3 Specimen Positioned for Measurement of Flexural and
specimen dimensions are: 75 mm in length, 15 mm in width,
Torsional Resonant Frequencies Using Thread or Wire Suspen-
sion
and3mminthickness.Suitablecylindricalroddimensionsare:
125 mm in length and 6 mm in diameter.
8.2.1 These specimen sizes should produce a fundamental
fundamental flexural node locations (0.224 L from each end).
flexural resonant frequency in the range from 1000 to 10000
The suspension point distances can be adjusted experimentally
Hzandafundamentaltorsionalresonantfrequencyintherange
tomaximizethevibrationaldeflectionandresultingsignal.For
from10000to30000Hz.(TypicalvaluesofYoung’smodulus
torsionalvibration,theaxesofsuspensionhavetobeoff-center
for different advanced ceramics are 360 GPa (52 × 10 psi) for
from the longitudinal axis of the specimen (shown in Fig. 3).
alumina (99%), 300 GPa (43 × 10 psi) for silicon nitride,
7.11 Specimen Supports—If the specimen is supported on
430GPa (62 × 10 psi) for silicon carbide, and 200 GPa (29 ×
direct-contact supports, the supports shall permit the specimen
10 psi) for zirconia.) Specimens shall have a minimum mass
to oscillate without significant restriction in the desired mode.
of 5g to avoid coupling effects; any size of specimen that has
This is accomplished for flexural modes by supporting the
a suitable length-to-cross-section ratio in terms of frequency
specimenatitstransversefundamentalnodelocations(0.224 L
response and meets the mass minimum may be used. Maxi-
from each end). In torsional modes the specimen should be
mum specimen size and mass are determined primarily by the
supportedatitscenterpoint.Thesupportsshouldhaveminimal
mechanicaldrivingpowerofthetestsystemandthelimitations
area in contact with the specimen and shall be cork, rubber, or
of the experimental configuration.
similar material. In order to properly identify resonant
8.3 Finish the surfaces of the specimen using a fine grind
frequencies, the transducers should be movable along the total
(400 grit or finer). All surfaces on the rectangular specimen
specimen length and width. (See Fig. 4.) The transducer
shall be flat. Opposite surfaces across the length and width
contact pressure should be consistent with good response and
shall be parallel within 0.01 mm or 60.1%, whichever is
minimal interference with the free vibration of the specimen.
greater. Opposite surfaces across the thickness shall be parallel
within 0.002 mm or 60.1%, whichever is greater. The
8. Test Specimen
cylindrical specimen shall be round and constant in diameter
8.1 Preparethespecimenssothattheyareeitherrectangular
within 0.002 mm or 60.1%, whichever is greater.
or circular in cross-section. Either geometry can be used to
measure both dynamic Young’s modulus and dynamic shear
8.4 Dry the specimen in air at 120°C in a drying oven until
modulus. However, experimental difficulties in obtaining tor- the mass is constant (less than 0.1% or 10 mg difference in
mass with 30 min of additional drying).
8.5 It is recommended that the laboratory obtain and main-
tain an internal reference specimen with known and recorded
fundamental resonant frequencies in flexure and torsion. The
referencespecimenmustmeetthesize,dimensionaltolerances,
and surface finish requirements of Section 8. The reference
specimenshouldbeusedtocheckandconfirmtheoperationof
the test system on a regular basis. It can also be used to train
operators in the proper test setup and signal analysis tech-
niques. The reference specimen can be a standard ceramic
(alumina, silicon carbide, zirconia, etc.) or metal material, or it
may be of a similar size, composition, properties, and micro-
FIG. 4 Specimen Positioned for Measurement of Flexural and
structuretothetypesofceramicspecimenscommonlytestedat
Torsional Resonant Frequencies Using Direct Support and Direct
Contact Transducers the laboratory.
C1198 − 20
9. Procedure
9.1 Procedure A – Room-Temperature Testing:
9.1.1 Switch on all electrical equipment and allow to
stabilize in accordance with the manufacturer’s recommenda-
tions.
9.1.2 Thedimensionsandmassofthetestspecimenmustbe
measured and recorded, either before or after the test. Measure
the mass to an accuracy of 610 mg or 60.1% (whichever is
greater). Measure the length of the test specimen to an
accuracy of 60.01 mm or 60.1% (whichever is greater). For
rectangular rods, measure the width dimensions to an accuracy
of 60.01 mm or 60.1% (whichever is greater) and the
thicknesstoanaccuracyof 60.002mmor 60.1%(whichever
FIG. 5 Dynamic Modulus Resonant Modes and Nodal Locations
Tracking Guide Template
is greater). Measure the width and thickness at three equally
spacedlocationsalongthelengthanddeterminetheaveragefor
9.1.4 Torsional Resonance:
each dimension. For cylindrical rods, measure the diameter to
an accuracy of 60.002 mm or 60.1% (whichever is greater) 9.1.4.1 If a determination of the shear modulus is desired,
offset the specimen supports/suspensions or transducer
at three equally spaced locations along the length and deter-
mine the average of the t
...

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: C1198 − 09 (Reapproved 2013) C1198 − 20
Standard Test Method for
Dynamic Young’s Modulus, Shear Modulus, and Poisson’s
Ratio for Advanced Ceramics by Sonic Resonance
This standard is issued under the fixed designation C1198; 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 Scope*
1.1 This test method covers the determination of the dynamic elastic properties of advanced ceramics. Specimens of these
materials possess specific mechanical resonant frequencies that are determined by the elastic modulus, mass, and geometry of the
test specimen. Therefore, the dynamic elastic properties of a material can be computed if the geometry, mass, and mechanical
resonant frequencies of a suitable rectangular or cylindrical test specimen of that material can be measured. The resonant
frequencies in flexure and torsion are measured by mechanical excitation of vibrations of the test specimen in a suspended mode
(Section 4 and Figs. 1 and 4). Dynamic Young’s modulus is determined using the resonant frequency in the flexural mode of
vibration. The dynamic shear modulus, or modulus of rigidity, is found using torsional resonant vibrations. Dynamic Young’s
modulus and dynamic shear modulus are used to compute Poisson’s ratio.
1.2 This test method measures the resonant frequencies of test specimens of suitable geometry by mechanically exciting them
at continuously variable frequencies. Mechanical excitation of the bars is provided through the use of a transducer that transforms
a cyclic electrical signal into a cyclic mechanical force on the specimen. A second transducer senses the resulting mechanical
vibrations of the specimen and transforms them into an electrical signal. The amplitude and frequency of the signal are measured
by an oscilloscope or other means to detect resonant vibration in the desired mode. The resonant frequencies, dimensions, and mass
of the specimen are used to calculate dynamic Young’s modulus and dynamic shear modulus. (See Fig. 1)
1.2 This test method is specifically appropriate for advanced ceramics that are elastic, homogeneous, and isotropic (1).
Advanced ceramics of a composite character (particulate, whisker, or fiber reinforced) may be tested by this test method with the
understanding that the character (volume fraction, size, morphology, distribution, orientation, elastic properties, and interfacial
bonding) of the reinforcement in the test specimen will have a direct effect on the elastic properties. These reinforcement effects
must be considered in interpreting the test results for composites. This test method is not satisfactory for specimens that have cracks
or voids that are major discontinuities in the specimen. Neither is the test method satisfactory when these materials cannot be
fabricated in a uniform rectangular or circular cross section.cross-section.
1.3 A high-temperature furnace and cryogenic cabinet are described for measuring the dynamic elastic moduli as a function of
temperature from −195 to 1200°C.1200 °C.
1.5 Modification of this test method for use in quality control is possible. A range of acceptable resonant frequencies is
determined for a specimen with a particular geometry and mass. Any specimen with a frequency response falling outside this
frequency range is rejected. The actual modulus of each specimen need not be determined as long as the limits of the selected
frequency range are known to include the resonant frequency that the specimen must possess if its geometry and mass are within
specified tolerances.
1.4 The procedures in this test method are, where possible, consistent with the procedures of There are material-specific ASTM
standards that cover the determination of resonance frequencies and elastic properties of specific materials by sonic resonance or
by impulse excitation of vibration. Test Methods C215, C623, C747, C848and, C848C1259., E1875The tables of, and E1876 these
test methods have been replaced by the actual formulas from the original references. With the advent of computers and
sophisticated hand calculators, the actual formulas can be easily used and provide greater accuracy than factor tables.may differ
from this test method in several areas (for example: sample size, dimensional tolerances, sample preparation, calculation details,
This test method is under the jurisdiction of ASTM Committee C28 on Advanced Ceramics and is the direct responsibility of Subcommittee C28.01 on Mechanical
Properties and Performance.
Current edition approved Aug. 1, 2013Jan. 1, 2020. Published September 2013January 2020. Originally approved in 1991. Last previous edition approved in 20092013
as C1198 – 09. 09 (2013). DOI: 10.1520/C1198-09R13.10.1520/C1198-20.
The boldface numbers given in parentheses refer to a list of references at the end of the text.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
C1198 − 20
etc.). The testing of those materials should be done in compliance with the appropriate material-specific standards. Where possible,
the procedures, sample specifications, and calculations in this standard are consistent with the other test methods.
1.5 The values stated in SI units are to be regarded as the standard. The non-SI values given in parentheses are for information
only. only and are not considered 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 safety, health, and healthenvironmental practices and determine the
applicability of regulatory limitations prior to use.
1.7 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.
2. Referenced Documents
2.1 ASTM Standards:
C215 Test Method for Fundamental Transverse, Longitudinal, and Torsional Resonant Frequencies of Concrete Specimens
C372 Test Method for Linear Thermal Expansion of Porcelain Enamel and Glaze Frits and Fired Ceramic Whiteware Products
by the Dilatometer Method
C623 Test Method for Young’s Modulus, Shear Modulus, and Poisson’s Ratio for Glass and Glass-Ceramics by Resonance
C747 Test Method for Moduli of Elasticity and Fundamental Frequencies of Carbon and Graphite Materials by Sonic Resonance
C848 Test Method for Young’s Modulus, Shear Modulus, and Poisson’s Ratio For Ceramic Whitewares by Resonance
C1145 Terminology of Advanced Ceramics
C1161 Test Method for Flexural Strength of Advanced Ceramics at Ambient Temperature
C1259 Test Method for Dynamic Young’s Modulus, Shear Modulus, and Poisson’s Ratio for Advanced Ceramics by Impulse
Excitation of Vibration
E6 Terminology Relating to Methods of Mechanical Testing
D4092E1875 Terminology Test Method for Plastics: Dynamic Mechanical PropertiesDynamic Young’s Modulus, Shear
Modulus, and Poisson’s Ratio by Sonic Resonance
E1876 Test Method for Dynamic Young’s Modulus, Shear Modulus, and Poisson’s Ratio by Impulse Excitation of Vibration
E2001 Guide for Resonant Ultrasound Spectroscopy for Defect Detection in Both Metallic and Non-metallic Parts
2.2 ISO Standard:
ISO 14704 Test Method for Flexural Strength of Monolithic Ceramics at Room Temperature
3. Terminology
3.1 Definitions:
3.1.1 advanced ceramic, n—a highly engineered, high performance, predominately nonmetallic, inorganic, ceramic material
having specific functional attributes. C1145
3.1.2 dynamic elastic modulus, n—the elastic modulus, either Young’s modulus or shear modulus, that is measured in a dynamic
mechanical measurement. E1876
3.1.3 advanced ceramic, dynamic mechanical measurement, n—a highly engineered, high performance, predominately
nonmetallic, inorganic, ceramic material having specific functional attributes. technique in which either the modulus or damping,
or both, of a substance under oscillatory load or displacement is measured as a function of temperature, frequency, or time, or
combination thereof. C1145E6
3.1.1.1 dynamic mechanical measurement, n—a technique in which either the modulus or damping, or both, of a substance
under oscillatory load or displacement is measured as a function of temperature, frequency, or time, or combination thereof. D4092
−2
3.1.4 elastic limit [FL ],n—the greatest stress that a material is capable of sustaining without permanent strain remaining upon
complete release of the stress. E6
−2
3.1.5 elastic modulus [FL ],n—the ratio of stress to strain below the proportional limit.
3.1.6 Poisson’s ratio (μ) [nd],n—the absolute value of the ratio of transverse strain to the corresponding axial strain resulting
from uniformly distributed axial stress below the proportional limit of the material. E6
3.1.6.1 Discussion—
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Available from International Organization for Standardization (ISO), ISO Central Secretariat, BIBC II, Chemin de Blandonnet 8, CP 401, 1214 Vernier, Geneva,
Switzerland, http://www.iso.org.
C1198 − 20
In isotropic materials Young’s modulus (E), shear modulus (G), and Poisson’s ratio (μ) are related by the following equation:
µ5 ~ E/2G ! 2 1
−2
3.1.7 proportional limit [FL ],n—the greatest stress that a material is capable of sustaining without deviation from
proportionality of stress to strain (Hooke’s law). E6
−2
3.1.8 shear modulus (G) [FL ],n—the elastic modulus in shear or torsion. Also called modulus of rigidity or torsional modulus.
E6
−2
3.1.9 Young’s modulus (E) [FL ],n—the elastic modulus in tension or compression. E6
3.2 Definitions of Terms Specific to This Standard:
3.2.1 anti-nodes, n—an unconstrained slender rod or bar in resonance contains two or more locations that have local maximum
displacements, called anti-nodes. For the fundamental flexure resonance, the anti-nodes are located at the two ends and the center
of the specimen.
3.2.2 elastic, adj—the property of a material such 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, that will be eliminated upon removal of the stress,
with the body returning instantly to its original size and shape without energy loss. Most advanced ceramics conform to this
definition well enough to make this resonance test valid.
3.2.3 flexural vibrations, n—the vibrations that occur when the oscillations in a slender rod or bar are in the plane normal to
the length dimension.
3.2.4 homogeneous, adj—the condition of a specimen such that the composition and density are uniform, such that any smaller
specimen taken from the original is representative of the whole. Practically, as long as the geometrical dimensions of the test
specimen are large with respect to the size of individual grains, crystals, or components, the body can be considered homogeneous.
3.2.5 isotropic, adj—the condition of a specimen such that the values of the elastic properties are the same in all directions in
the material. Advanced ceramics are considered isotropic on a macroscopic scale, if they are homogeneous and there is a random
distribution and orientation of phases, crystallites, and components.
3.2.6 nodes, n—a slender rod or bar in resonance contains one or more locations having a constant zero displacement, called
nodes. For the fundamental flexural resonance, the nodes are located at 0.224 L from each end, where L is the length of the
specimen.
3.2.7 resonance, n—a slender rod or bar driven into one of the modes of vibration described in 3.2.3 or 3.2.9 is said to be in
resonance when the imposed frequency is such that the resultant displacements for a given amount of driving force are at a
maximum. The resonant frequencies are natural vibration frequencies that are determined by the elastic modulus, mass, and
dimensions of the test specimen.
3.2.8 slender rod or bar, n—in dynamic elastic property testing, a specimen whose ratio of length to minimum cross-sectional
dimension is at least five and preferably in the range of 20 to 25.
3.2.9 torsional vibrations, n—the vibrations that occur when the oscillations in each cross-sectional plane of a slender rod or
bar are such that the plane twists around the length dimension axis.
4. Summary of Test Method
4.1 This test method measures the resonant frequencies of test specimens of suitable geometry by exciting them at continuously
variable frequencies. Mechanical excitation of the bars is provided through the use of a transducer that transforms a cyclic electrical
signal into a cyclic mechanical force on the specimen. A second transducer senses the resulting mechanical vibrations of the
specimen and transforms them into an electrical signal. The amplitude and frequency of the signal are measured by an oscilloscope
or other means to detect resonance. The resonant frequencies, dimensions, and mass of the specimen are used to calculate dynamic
Young’s modulus and dynamic shear modulus.
5. Significance and Use
5.1 This test method may be used for material development, characterization, design data generation, and quality control
purposes. It is specifically appropriate for determining the modulus of advanced ceramics that are elastic, homogeneous, and
isotropic.
5.1.1 This test method is nondestructive in nature. Only minute stresses are applied to the specimen, thus minimizing the
possibility of fracture.
5.1.2 The period of time during which measurement stress is applied and removed is of the order of hundreds of microseconds.
With this test method it is feasible to perform measurements at high temperatures, where delayed elastic and creep effects would
invalidate modulus measurements calculated from static loading.
5.2 This test method has advantages in certain respects over the use of static loading systems for measuring moduli in advanced
ceramics. It is nondestructive in nature and can be used for specimens prepared for other tests. Specimens are subjected to minute
strains; hence, the moduli are measured at or near the origin of the stress-strain curve with the minimum possibility of fracture.
C1198 − 20
The period of time during which measurement stress is applied and removed is of the order of hundreds of microseconds. With
this test method it is feasible to perform measurements at high temperatures, where delayed elastic and creep effects would
invalidate modulus measurements calculated from static loading.
5.3 The sonic resonant frequency technique can also be used as a nondestructive evaluation tool for detecting and screening
defects (cracks, voids, porosity, density variations) in ceramic parts. These defects may change the elastic response and the
observed resonant frequency of the test specimen. Guide E2001 describes a procedure for detecting such defects in metallic and
nonmetallic parts using the resonant frequency method.
5.4 Modification of this test method for use in quality control is possible. A range of acceptable resonant frequencies is
determined for a specimen with a particular geometry and mass. Any specimen with a frequency response falling outside this
frequency range is rejected. The actual modulus of each specimen need not be determined as long as the limits of the selected
frequency range are known to include the resonant frequency that the specimen must possess if its geometry and mass are within
specified tolerances.
6. Interferences
6.1 The relationships between resonant frequency and dynamic modulus presented herein are specifically applicable to
homogeneous, elastic, isotropic materials.
6.1.1 This test method of determining the moduli is applicable to composite ceramics and inhomogeneous materials only with
careful consideration of the effect of inhomogeneities and anisotropy. The character (volume fraction, size, morphology,
distribution, orientation, elastic properties, and interfacial bonding) of the reinforcement/inhomogeneities in the specimens will
have a direct effect on the elastic properties of the specimen as a whole. These effects must be considered in interpreting the test
results for composites and inhomogeneous materials.
6.1.2 If specific surface treatments (coatings, machining, grinding, etching, etc.) change the elastic properties of the near-surface
material, there will be accentuated effects on the properties measured by this flexural method, as compared to static/bulk
measurements by tensile or compression testing.
6.1.3 This test method is not satisfactory for specimens that have major discontinuities, such as large cracks (internal or surface)
or voids.
6.2 This test method for determining moduli is limited to specimens with regular geometries (rectangular parallelepiped and
cylinders) for which analytical equations are available to relate geometry, mass, and modulus to the resonant vibration frequencies.
This test method is not appropriate for determining the elastic properties of materials which cannot be fabricated into such
geometries.
6.2.1 The analytical equations assume parallel/concentric dimensions for the regular geometries of the specimen. Deviations
from the specified tolerances for the dimensions of the specimens will change the resonant frequencies and introduce error into
the calculations.
6.2.2 Edge treatments such as chamfers or radii are not considered in the analytical equations. Edge chamfers on flexure bars
prepared according to Test Method C1161 will change the resonant frequency of the test bars and introduce error into the
calculations of the dynamic modulus. It is recommended that specimens for this test not have chamfered or rounded edges.
Alternately, if narrow rectangular specimens with chamfers or edge radii are tested, then the procedures in Annex A1 should be
used to correct the calculated Young’s modulus, E.
6.2.3 For specimens with as-fabricated/rough or uneven surfaces, variations in dimension can have a significant effect in the
calculations. For example, in the calculation of the dynamic modulus, the modulus value is inversely proportional to the cube of
the thickness. Uniform specimen dimensions and precise measurements are essential for accurate results.
7. Apparatus
7.1 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 (preferably digital) monitors the audio oscillator output to provide an accurate frequency determination. A suitable
suspension-coupling system supports the test specimen. Another transducer acts to detect mechanical vibration in the specimen and
to convert it into an electrical signal that is passed through an amplifier and displayed on an indicating meter. The meter may be
a voltmeter, microammeter, or oscilloscope. An oscilloscope is recommended because it enables the operator to positively identify
resonances, including higher order higher-order harmonics, by Lissajous figure analysis. 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:
7.2 Audio Oscillator, having a continuously variable frequency output from about 100 Hz to at least 30 kHz. Frequency drift
shall not exceed 1 Hz/min for any given setting.
7.3 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.
C1198 − 20
FIG. 1 Block Diagram of a Typical Test Apparatus
7.4 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 photograph cartridge. A capacitive pickup may be
used if desired. An electromagnetic coupling system with an attached metal foil may also be used, with due consideration for effects
of the foil on the natural vibration of the test bar. The frequency response of the transducer across the frequency range of interest
shall have at least a 6.5 kHz 6.5-kHz bandwidth before −3 dB power loss occurs.
7.5 Power Amplifier, in the detector circuit shall be impedance matched with the type of detector transducer selected and shall
serve as a prescope amplifier.
7.6 Cathode-Ray Oscilloscope, any model suitable for general laboratory work.
7.7 Frequency Counter, preferably digital, shall be able to measure frequencies to within6 1within 61 Hz.
7.8 Furnace—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 large enough for the specimen to be uniform in temperature within 65°C65 °C along its
length through the range of temperatures encountered in testing. It is recommended that an independent thermocouple be placed
in close proximity to (within 5 mm), but not touching, the center of the specimen to accurately measure temperature during heating
and cooling.
7.9 Cryogenic Chamber—For data at cryogenic temperatures, any chamber shall suffice that shall be capable of controlled
heating/cooling, frost-freefrost-free, and uniform in temperature within 6 5°C 65 °C over the length of the specimen at any
selected temperature. A suitable cryogenic chamber is shown in Fig. 2 (2). It is recommended that an independent thermocouple
be placed in close proximity to (within 5 mm), but not touching, the center of the specimen to accurately measure temperature
during heating and cooling.
7.10 Specimen Suspension—Any method of specimen suspension shall be used that is adequate for the temperatures
encountered in testing and that allows the specimen to vibrate without significant restriction. Thread suspension is the system of
choice for cryogenic and high-temperature testing. (See Fig. 1 and Fig. 3.) Common cotton thread, silica-glass fiber thread,
oxidation-resistant nickel (or platinum) alloy wire, 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. The specimen should be initially suspended at distances of approximately 0.1 L from each end. The
specimen should not be suspended at its fundamental flexural node locations (0.224 L from each end). The suspension point
distances can be adjusted experimentally to maximize the vibrational deflection and resulting signal. For torsional vibration, the
axes of suspension have to be off-center from the longitudinal axis of the specimen (shown in Fig. 3).
7.11 Specimen Supports—If the specimen is supported on direct contact direct-contact supports, the supports shall permit the
specimen to oscillate without significant restriction in the desired mode. This is accomplished for flexural modes by supporting
the specimen at its transverse fundamental node locations (0.224 L from each end). In torsional modes the specimen should be
supported at its center point. The supports should have minimal area in contact with the specimen and shall be cork, rubber, or
similar material. In order to properly identify resonant frequencies, the transducers should be movable along the total specimen
length and width. (See Fig. 4.) The transducer contact pressure should be consistent with good response and minimal interference
with the free vibration of the specimen.
C1198 − 20
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 DetailDetailed Drawing of a Typical Cryogenic Chamber
FIG. 3 Specimen Positioned for Measurement of Flexural and Torsional Resonant Frequencies Using Thread or Wire Suspension
FIG. 4 Specimen Positioned for Measurement of Flexural and Torsional Resonant Frequencies Using Direct Support and Direct Contact
Transducers
8. Test Specimen
8.1 Prepare the specimens so that they are either rectangular or circular in cross section. cross-section. Either geometry can be
used to measure both dynamic Young’s modulus and dynamic shear modulus. However, experimental difficulties in obtaining
C1198 − 20
torsional resonant 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
rectangular bar.
8.2 Resonant frequencies for a given specimen are functions of the bar dimensions as well as its mass and moduli; therefore,
dimensions should be selected with this relationship in mind. Make selection of size so that, for an estimated modulus, the resonant
frequencies measured will fall within the range of frequency response of the transducers used. A slender rod with a ratio of length
to minimum cross-sectional dimension greater than ten and approximately 25 is preferred for ease in calculation. For shear
modulus measurements of rectangular bars, a ratio of width to thickness of five is recommended for minimizing experimental
difficulties. Suitable rectangular specimen dimensions are: 75 mm in length, 15 mm in width, and 3 mm in thickness. Suitable
cylindrical rod dimensions are: 125 mm in length and 6 mm in diameter.
8.2.1 These specimen sizes should produce a fundamental flexural resonant frequency in the range from 1000 to 10 000 Hz and
a fundamental torsional resonant frequency in the range from 10 000 to 30 000 Hz. (Typical values of Young’s modulus for
6 6
different advanced ceramics are 360 GPa (52 × 10 psi) for alumina (99 %), 300 GPa (43 × 10 psi) for silicon nitride, 430 GPa
6 6
430 GPa (62 × 10 psi) for silicon carbide, and 200 GPa (29 × 10 psi) for zirconia.) Specimens shall have a minimum mass of
5 g 5 g to avoid coupling effects; any size of specimen that has a suitable length-to-cross section 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 mechanical driving power of the test system and the limitations of the experimental configuration.
8.3 Finish the surfaces of the specimen using a fine grind (400 grit or finer). All surfaces on the rectangular specimen shall be
flat. Opposite surfaces across the length and width shall be parallel within 0.01 mm or 60.1 %60.1 %, whichever is greater.
Opposite surfaces across the thickness shall be parallel within 0.002 mm or 6 0.1 % 60.1 %, whichever is greater. The cylindrical
specimen shall be round and constant in diameter within 0.002 mm or 6 0.1 % 60.1 %, whichever is greater.
8.4 Dry the specimen in air at 120°C120 °C in a drying oven until the mass is constant (less than 0.1 % or 10 mg difference
in mass with 30 min of additional drying).
8.5 It is recommended that the laboratory obtain and maintain an internal reference specimen with known and recorded
fundamental resonant frequencies in flexure and torsion. The reference specimen must meet the size, dimensional tolerances, and
surface finish requirements of Section 8. The reference specimen should be used to check and confirm the operation of the test
system on a regular basis. It can also be used to train operators in the proper test setup and signal analysis techniques. The reference
specimen can be a standard ceramic (alumina, silicon carbide, zirconia, etc.) or metal material, or it may be of a similar size,
composition, properties, and microstructure to the types of ceramic specimens commonly tested at the laboratory.
9. Procedure
9.1 Procedure A—Room-Temperature A – Room-Temperature Testing:
9.1.1 Switch on all electrical equipment and allow to stabilize in accordance with the manufacturer’s recommendations.
9.1.2 The dimensions and mass of the test specimen must be measured and recorded, either before or after the test. Measure
the mass to an accuracy of 610 mg or 60.1 % (whichever is greater). Measure the length of the test specimen to an accuracy of
6 0.01 60.01 mm or 6 0.1 % 60.1 % (whichever is greater). For rectangular rods, measure the width dimensions to an accuracy
of 60.01 mm or 60.1 % (whichever is greater) and the thickness to an accuracy of 60.002 mm or 60.1 % (whichever is greater).
Measure the width and thickness at three equally spaced locations along the length and determine the average for each dimension.
For cylindrical rods, measure the diameter to an accuracy of 60.002 mm or 60.1 % (whichever is greater) at three equally spaced
locations along the length and determine the average of the three measurements.
9.1.3 Flexural ResonanceResonance:
9.1.3.1 Suspend or support the specimen and position the transducers to induce and detect flexural resonance, as shown in Fig.
3 or Fig. 4.
9.1.3.2 Activate the oscillator and the driving transducer with sufficient power to excite the desired vibration in the test
specimen. 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.
9.1.3.3 Scan frequencies with the audio oscillator until specimen flexural resonance is indicated by a sinusoidal pattern of
maximum amplitude on the oscilloscope or by a single closed loop closed-loop Lissajous pattern. (It is recommended that the
frequency scan start at a low frequency and then increase.)
9.1.3.4 To verify that the measured frequency is fundamental and not an overtone, identify either the node/anti-node locations
or one or more overtones (see Note 1).
NOTE 1—The proper identification of the fundamental flexural mode is important as spurious frequencies i
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