ASTM C1198-96

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

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 test specimen of that material can be measured. 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). 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 1200oC.
1.4 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.
1.5 The procedures in this test method are, where possible, consistent with the procedures of Test Methods C623, C747, and C848. The tables of 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.
1.6 The values stated in SI units are to be regarded as the standard. The values given in parentheses are for information only.
1.7 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.

General Information

• Status: Historical
• Publication Date: 09-Apr-2001
• ICS: 81.060.30 - Advanced ceramics
• Technical Committee: C28 - Advanced Ceramics
• Drafting Committee: C28.01 - Mechanical Properties and Performance

Relations

• Replaced By: ASTM C1198-01 - Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio for Advanced Ceramics by Sonic Resonance
• Effective Date: 10-Apr-2001
• Referred By: ASTM C1836-16(2023) - Standard Classification for Fiber Reinforced Carbon-Carbon Composite Structures
• Effective Date: 10-Apr-2001
• Referred By: ASTM C1259-21 - Standard Test Method for Dynamic Young’s Modulus, Shear Modulus, and Poisson’s Ratio for Advanced Ceramics by Impulse Excitation of Vibration
• Effective Date: 10-Apr-2001
• Referred By: ASTM C1835-16(2023) - Standard Classification for Fiber Reinforced Silicon Carbide-Silicon Carbide (SiC-SiC) Composite Structures
• Effective Date: 10-Apr-2001
• Referred By: ASTM F2393-12(2020) - Standard Specification for High-Purity Dense Magnesia Partially Stabilized Zirconia (Mg-PSZ) for Surgical Implant Applications
• Effective Date: 10-Apr-2001
• Referred By: ASTM C1674-23 - Standard Test Method for Flexural Strength of Advanced Ceramics with Engineered Porosity (Honeycomb Cellular Channels) at Ambient Temperatures
• Effective Date: 10-Apr-2001
• Referred By: ASTM E1875-20a - Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Sonic Resonance
• Effective Date: 10-Apr-2001
• Referred By: ASTM E1876-22 - Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Impulse Excitation of Vibration
• Effective Date: 10-Apr-2001
• Referred By: ASTM C1793-15 - Standard Guide for Development of Specifications for Fiber Reinforced Silicon Carbide-Silicon Carbide Composite Structures for Nuclear Applications
• Effective Date: 10-Apr-2001
• Referred By: ASTM C1783-15 - Standard Guide for Development of Specifications for Fiber Reinforced Carbon-Carbon Composite Structures for Nuclear Applications
• Effective Date: 10-Apr-2001
• Referred By: ASTM F561-19 - Standard Practice for Retrieval and Analysis of Medical Devices, and Associated Tissues and Fluids
• Effective Date: 10-Apr-2001
• Referred By: ASTM F603-12(2020) - Standard Specification for High-Purity Dense Aluminum Oxide for Medical Application
• Effective Date: 10-Apr-2001

Standards Content (Sample)

NOTICE: This standard has either been superseded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
Designation: C 1198 – 96
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 C 1198; 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 (e) indicates an editorial change since the last revision or reapproval.
1. Scope selected frequency range are known to include the resonant
frequency that the specimen must possess if its geometry and
1.1 This test method covers the determination of the dy-
mass are within specified tolerances.
namic elastic properties of advanced ceramics. Specimens of
1.5 The procedures in this test method are, where possible,
these materials possess specific mechanical resonant frequen-
consistent with the procedures of Test Methods C 623, C 747,
cies that are determined by the elastic modulus, mass, and
and C 848. The tables of these test methods have been replaced
geometry of the test specimen. Therefore, the dynamic elastic
by the actual formulas from the original references. With the
properties of a material can be computed if the geometry, mass,
advent of computers and sophisticated hand calculators, the
and mechanical resonant frequencies of a suitable test speci-
actual formulas can be easily used and provide greater accu-
men of that material can be measured. Dynamic Young’s
racy than factor tables.
modulus is determined using the resonant frequency in the
1.6 The values stated in SI units are to be regarded as the
flexural mode of vibration. The dynamic shear modulus, or
standard. The values given in parentheses are for information
modulus of rigidity, is found using torsional resonant vibra-
only.
tions. Dynamic Young’s modulus and dynamic shear modulus
1.7 This standard does not purport to address all of the
are used to compute Poisson’s ratio.
safety concerns, if any, associated with its use. It is the
1.2 This test method is specifically appropriate for advanced
responsibility of the user of this standard to establish appro-
ceramics that are elastic, homogeneous, and isotropic (1).
priate safety and health practices and determine the applica-
Advanced ceramics of a composite character (particulate,
bility of regulatory limitations prior to use.
whisker, or fiber reinforced) may be tested by this test method
with the understanding that the character (volume fraction,
2. Referenced Documents
size, morphology, distribution, orientation, elastic properties,
2.1 ASTM Standards:
and interfacial bonding) of the reinforcement in the test
C 372 Test Method for Linear Thermal Expansion of Por-
specimen will have a direct effect on the elastic properties.
celain Enamel and Glaze Frits and Fired Ceramic Whitew-
These reinforcement effects must be considered in interpreting
are Products by the Dilatomer Method
the test results for composites. This test method is not
C 623 Test Method for Young’s Modulus, Shear Modulus,
satisfactory for specimens that have cracks or voids that are
and Poisson’s Ratio for Glass and Glass-Ceramics by
major discontinuities in the specimen. Neither is the test
Resonance
method satisfactory when these materials cannot be fabricated
C 747 Test Method for Moduli of Elasticity and Fundamen-
in a uniform rectangular or circular cross section.
tal Frequencies of Carbon and Graphite Materials by Sonic
1.3 A high-temperature furnace and cryogenic cabinet are
Resonance
described for measuring the dynamic elastic moduli as a
C 848 Test Method for Young’s Modulus, Shear Modulus,
function of temperature from −195 to 1200°C.
and Poisson’s Ratio for Ceramic Whitewares by Reso-
1.4 Modification of this test method for use in quality
nance
control is possible. A range of acceptable resonant frequencies
C 1145 Terminology of Advanced Ceramics
is determined for a specimen with a particular geometry and
C 1161 Test Method for Flexural Strength of Advanced
mass. Any specimen with a frequency response falling outside
Ceramics at Ambient Temperatures
this frequency range is rejected. The actual modulus of each
D 4092 Terminology Relating to Dynamic Mechanical
specimen need not be determined as long as the limits of the
Measurements on Plastics
1 3. Terminology
This test method is under the jurisdiction of ASTM Committee C-28 on
Advanced Ceramics and is the direct responsibility of Subcommittee C28.01 on
3.1 Definitions:
Properties and Performance.
Current edition approved June 10, 1996. Published August 1996. Originally
published as C 1198 – 91. Last previous edition C 1198 – 91. Annual Book of ASTM Standards, Vol 15.02.
2 4
The boldface numbers given in parentheses refer to a list of references at the Annual Book of ASTM Standards, Vol 15.01.
end of the text. Annual Book of ASTM Standards, Vol 08.02.
Copyright © ASTM, 100 Barr Harbor Drive, West Conshohocken, PA 19428-2959, United States.
C 1198
3.1.1 advanced ceramic, n—a highly engineered, high per- random distribution and orientation of phases, crystallites, and
formance, predominately nonmetallic, inorganic, ceramic ma- components.
terial having specific functional attributes. (C 1145) 3.2.6 nodes, n—a slender rod or bar in resonance contains
one or more locations having a constant zero displacement,
3.1.2 dynamic mechanical measurement, n—a technique in
which either the modulus or damping, or both, of a substance called nodes. For the fundamental flexural resonance, the nodes
are located at 0.224 L from each end, where L is the length of
under oscillatory load or displacement is measured as a
function of temperature, frequency, or time, or combination the specimen.
3.2.7 resonance, n—a slender rod or bar driven into one of
thereof. (D 4092)
−2
3.1.3 elastic limit [FL ], n—the greatest stress that a 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
material is capable of sustaining without permanent strain
remaining upon complete release of the stress. resultant displacements for a given amount of driving force are
−2
at a maximum. The resonant frequencies are natural vibration
3.1.4 elastic modulus [FL ], n—the ratio of stress to strain
frequencies that are determined by the elastic modulus, mass,
below the proportional limit.
and dimensions of the test specimen.
3.1.5 Poisson’s ratio (μ) [nd], n—the absolute value of the
3.2.8 slender rod or bar, n—in dynamic elastic property
ratio of transverse strain to the corresponding axial strain
testing, a specimen whose ratio of length to minimum cross-
resulting from uniformly distributed axial stress below the
sectional dimension is at least five and preferably in the range
proportional limit of the material.
of 20 to 25.
3.1.6 Discussion—In isotropic materials Young’s modulus
3.2.9 torsional vibrations, n— the vibrations that occur
(E), shear modulus (G), and Poisson’s ratio (μ) are related by
when the oscillations in each cross-sectional plane of a slender
the following equation:
rod or bar are such that the plane twists around the length
μ 5 ~ E/2G ! 2 1 (1)
dimension axis.
−2
3.1.7 proportional limit [FL ], n—the greatest stress that a 4. Summary of Test Method
material is capable of sustaining without deviation from
4.1 This test method measures the resonant frequencies of
proportionality of stress to strain (Hooke’s law).
test specimens of suitable geometry by exciting them at
−2
3.1.8 shear modulus (G) [FL ], n—the elastic modulus in
continuously variable frequencies. Mechanical excitation of
shear or torsion. Also called modulus of rigidity or torsional
the bars is provided through the use of a transducer that
modulus.
transforms a cyclic electrical signal into a cyclic mechanical
−2
3.1.9 Young’s modulus ( E) [FL ], n—the elastic modulus
force on the specimen. A second transducer senses the resulting
in tension or compression.
mechanical vibrations of the specimen and transforms them
3.2 Definitions of Terms Specific to This Standard:
into an electrical signal. The amplitude and frequency of the
3.2.1 anti-nodes, n—an unconstrained slender rod or bar in
signal are measured by an oscilloscope or other means to detect
resonance contains two or more locations that have local
resonance. The resonant frequencies, dimensions, and mass of
maximum displacements, called anti-nodes. For the fundamen-
the specimen are used to calculate dynamic Young’s modulus
tal flexure resonance, the anti-nodes are located at the two ends
and dynamic shear modulus.
and the center of the specimen.
5. Significance and Use
3.2.2 elastic, adj—the property of a material such that an
application of stress within the elastic limit of that material
5.1 This test method may be used for material development,
making up the body being stressed will cause an instantaneous
characterization, design data generation, and quality control
and uniform deformation, that will be eliminated upon removal
purposes. It is specifically appropriate for determining the
of the stress, with the body returning instantly to its original
modulus of advanced ceramics that are elastic, homogeneous,
size and shape without energy loss. Most advanced ceramics
and isotropic.
conform to this definition well enough to make this resonance
5.1.1 This test method is nondestructive in nature. Only
test valid.
minute stresses are applied to the specimen, thus minimizing
3.2.3 flexural vibrations, n—the vibrations that occur when
the possibility of fracture.
the oscillations in a slender rod or bar are in the plane normal
5.1.2 The period of time during which measurement stress
to the length dimension.
is applied and removed is of the order of hundreds of
3.2.4 homogeneous, adj—the condition of a specimen such microseconds. With this test method it is feasible to perform
that the composition and density are uniform, such that any
measurements at high temperatures, where delayed elastic and
smaller specimen taken from the original is representative of creep effects would invalidate modulus measurements calcu-
the whole. Practically, as long as the geometrical dimensions of lated from static loading.
the test specimen are large with respect to the size of individual
5.2 This test method has advantages in certain respects over
grains, crystals, or components, the body can be considered the use of static loading systems for measuring moduli in
homogeneous.
advanced ceramics. It is nondestructive in nature and can be
3.2.5 isotropic, adj—the condition of a specimen such that used for specimens prepared for other tests. Specimens are
the values of the elastic properties are the same in all directions subjected to minute strains; hence, the moduli are measured at
in the material. Advanced ceramics are considered isotropic on or near the origin of the stress-strain curve with the minimum
a macroscopic scale, if they are homogeneous and there is a possibility of fracture. The period of time during which
C 1198
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 measure-
ments calculated from static loading.
6. Interferences
6.1 The relationships between resonant frequency and dy-
namic modulus presented herein are specifically applicable to
homogeneous, elastic, isotropic materials.
6.1.1 This test method of determining the moduli is appli-
cable to composite ceramics and inhomogeneous materials
only with careful consideration of the effect of inhomogeneities
and anisotropy. The character (volume fraction, size, morphol-
ogy, distribution, orientation, elastic properties, and interfacial
FIG. 1 Block Diagram of a Typical Test Apparatus
bonding) of the reinforcement/inhomogeneities in the speci-
mens will have a direct effect on the elastic properties of the
A frequency meter (preferably digital) monitors the audio
specimen as a whole. These effects must be considered in
oscillator output to provide an accurate frequency determina-
interpreting the test results for composites and inhomogeneous
tion. A suitable suspension-coupling system supports the test
materials.
specimen. Another transducer acts to detect mechanical vibra-
6.1.2 If specific surface treatments (coatings, machining,
tion in the specimen and to convert it into an electrical signal
grinding, etching, etc.) change the elastic properties of the
that is passed through an amplifier and displayed on an
near-surface material, there will be accentuated effects on the
indicating meter. The meter may be a voltmeter, microamme-
properties measured by this flexural method, as compared to
ter, or oscilloscope. An oscilloscope is recommended because
static/bulk measurements by tensile or compression testing.
it enables the operator to positively identify resonances,
6.1.3 This test method is not satisfactory for specimens that
including higher order harmonics, by Lissajous figure analysis.
have major discontinuities, such as large cracks (internal or
If a Lissajous figure is desired, the output of the oscillator is
surface) or voids.
6.2 This test method for determining moduli is limited to also coupled to the horizontal plates of the oscilloscope. If
temperature-dependent data are desired, a suitable furnace or
specimens with regular geometries (rectangular parallelepiped
and cylinders) for which analytical equations are available to cryogenic chamber is used. Details of the equipment are as
follows:
relate geometry, mass, and modulus to the resonant vibration
7.2 Audio Oscillator, having a continuously variable fre-
frequencies. This test method is not appropriate for determin-
quency output from about 100 Hz to at least 30 kHz. Frequency
ing the elastic properties of materials which cannot be fabri-
drift shall not exceed 1 Hz/min for any given setting.
cated into such geometries.
7.3 Audio Amplifier, having a power output sufficient to
6.2.1 The analytical equations assume parallel/concentric
ensure that the type of transducer used can excite any specimen
dimensions for the regular geometries of the specimen. Devia-
the mass of which falls within a specified range.
tions from the specified tolerances for the dimensions of the
7.4 Transducers—Two are required; one used as a driver
specimens will change the resonant frequencies and introduce
may be a speaker of the tweeter type or a magnetic cutting head
error into the calculations.
or other similar device depending on the type of coupling
6.2.2 Edge treatments such as chamfers or radii are not
chosen for use between the tran
...