ASTM C1198-09(2013)
(Test Method)Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio for Advanced Ceramics by Sonic Resonance
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.
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 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)
1.3 This test method is specifically appropriate for advanced ceramics that are elastic, homogeneous, and isotropic (3).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 te...
General Information
Relations
Standards Content (Sample)
NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: C1198 − 09 (Reapproved 2013)
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 Advanced ceramics of a composite character (particulate,
whisker, or fiber reinforced) may be tested by this test method
1.1 This test method covers the determination of the dy-
with the understanding that the character (volume fraction,
namic elastic properties of advanced ceramics. Specimens of
size, morphology, distribution, orientation, elastic properties,
these materials possess specific mechanical resonant frequen-
and interfacial bonding) of the reinforcement in the test
cies that are determined by the elastic modulus, mass, and
specimen will have a direct effect on the elastic properties.
geometry of the test specimen. Therefore, the dynamic elastic
These reinforcement effects must be considered in interpreting
propertiesofamaterialcanbecomputedifthegeometry,mass,
the test results for composites. This test method is not
and mechanical resonant frequencies of a suitable test speci-
satisfactory for specimens that have cracks or voids that are
men of that material can be measured. Dynamic Young’s
major discontinuities in the specimen. Neither is the test
modulus is determined using the resonant frequency in the
method satisfactory when these materials cannot be fabricated
flexural mode of vibration. The dynamic shear modulus, or
in a uniform rectangular or circular cross section.
modulus of rigidity, is found using torsional resonant vibra-
tions. Dynamic Young’s modulus and dynamic shear modulus 1.4 A high-temperature furnace and cryogenic cabinet are
are used to compute Poisson’s ratio.
described for measuring the dynamic elastic moduli as a
function of temperature from −195 to 1200°C.
1.2 This test method measures the resonant frequencies of
test specimens of suitable geometry by mechanically exciting
1.5 Modification of this test method for use in quality
them at continuously variable frequencies. Mechanical excita-
control is possible.Arange of acceptable resonant frequencies
tion of the bars is provided through the use of a transducer that
is determined for a specimen with a particular geometry and
transforms a cyclic electrical signal into a cyclic mechanical
mass.Any specimen with a frequency response falling outside
forceonthespecimen.Asecondtransducersensestheresulting
this frequency range is rejected. The actual modulus of each
mechanical vibrations of the specimen and transforms them
specimen need not be determined as long as the limits of the
into an electrical signal. The amplitude and frequency of the
selected frequency range are known to include the resonant
signalaremeasuredbyanoscilloscopeorothermeanstodetect
frequency that the specimen must possess if its geometry and
resonant vibration in the desired mode. The resonant
mass are within specified tolerances.
frequencies, dimensions, and mass of the specimen are used to
1.6 The procedures in this test method are, where possible,
calculate dynamicYoung’s modulus and dynamic shear modu-
consistent with the procedures of Test Methods C623, C747,
lus. (See Fig. 1)
and C848.The tables of these test methods have been replaced
1.3 Thistestmethodisspecificallyappropriateforadvanced
by the actual formulas from the original references. With the
ceramics that are elastic, homogeneous, and isotropic (1).
advent of computers and sophisticated hand calculators, the
actual formulas can be easily used and provide greater accu-
racy than factor tables.
This test method is under the jurisdiction of ASTM Committee C28 on
Advanced Ceramics and is the direct responsibility of Subcommittee C28.01 on
1.7 The values stated in SI units are to be regarded as the
Mechanical Properties and Performance.
standard. The values given in parentheses are for information
Current edition approved Aug. 1, 2013. Published September 2013. Originally
approved in 1991. Last previous edition approved in 2009 as C1198– 09. DOI:
only.
10.1520/C1198-09R13.
1.8 This standard does not purport to address all of the
The boldface numbers given in parentheses refer to a list of references at the
end of the text. safety concerns, if any, associated with its use. It is the
Copyright ©ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA19428-2959. United States
C1198 − 09 (2013)
−2
responsibility of the user of this standard to establish appro- 3.1.6 shear modulus (G) [FL ],n—the elastic modulus in
priate safety and health practices and determine the applica- shear or torsion. Also called modulus of rigidity or torsional
bility of regulatory limitations prior to use. modulus.
−2
3.1.7 Young’s modulus( E)[FL ],n—theelasticmodulusin
2. Referenced Documents
tension or compression.
2.1 ASTM Standards:
3.2 Definitions of Terms Specific to This Standard:
C372Test Method for Linear Thermal Expansion of Porce-
3.2.1 anti-nodes, n—an unconstrained slender rod or bar in
lainEnamelandGlazeFritsandFiredCeramicWhiteware
resonance contains two or more locations that have local
Products by the Dilatometer Method
maximumdisplacements,calledanti-nodes.Forthefundamen-
C623Test Method for Young’s Modulus, Shear Modulus,
talflexureresonance,theanti-nodesarelocatedatthetwoends
and Poisson’s Ratio for Glass and Glass-Ceramics by
and the center of the specimen.
Resonance
C747TestMethodforModuliofElasticityandFundamental 3.2.2 elastic, adj—the property of a material such that an
Frequencies of Carbon and Graphite Materials by Sonic
application of stress within the elastic limit of that material
Resonance making up the body being stressed will cause an instantaneous
C848Test Method for Young’s Modulus, Shear Modulus,
anduniformdeformation,thatwillbeeliminateduponremoval
and Poisson’s Ratio For Ceramic Whitewares by Reso- of the stress, with the body returning instantly to its original
nance
size and shape without energy loss. Most advanced ceramics
C1145Terminology of Advanced Ceramics
conform to this definition well enough to make this resonance
C1161Test Method for Flexural Strength of Advanced
test valid.
Ceramics at Ambient Temperature
3.2.3 flexural vibrations, n—the vibrations that occur when
D4092 Terminology for Plastics: Dynamic Mechanical
the oscillations in a slender rod or bar are in the plane normal
Properties
to the length dimension.
E2001Guide for Resonant Ultrasound Spectroscopy for
3.2.4 homogeneous, adj—the condition of a specimen such
Defect Detection in Both Metallic and Non-metallic Parts
that the composition and density are uniform, such that any
3. Terminology smaller specimen taken from the original is representative of
thewhole.Practically,aslongasthegeometricaldimensionsof
3.1 Definitions:
thetestspecimenarelargewithrespecttothesizeofindividual
3.1.1 advanced ceramic, n—a highly engineered, high
grains, crystals, or components, the body can be considered
performance, predominately nonmetallic, inorganic, ceramic
homogeneous.
material having specific functional attributes. C1145
3.2.5 isotropic, adj—the condition of a specimen such that
3.1.1.1 dynamic mechanical measurement, n—a technique
thevaluesoftheelasticpropertiesarethesameinalldirections
inwhicheitherthemodulusordamping,orboth,ofasubstance
in the material.Advanced ceramics are considered isotropic on
under oscillatory load or displacement is measured as a
a macroscopic scale, if they are homogeneous and there is a
function of temperature, frequency, or time, or combination
random distribution and orientation of phases, crystallites, and
thereof. D4092
components.
−2
3.1.2 elastic limit [FL ],n—the greatest stress that a
3.2.6 nodes, n—a slender rod or bar in resonance contains
material is capable of sustaining without permanent strain
one or more locations having a constant zero displacement,
remaining upon complete release of the stress.
−2 callednodes.Forthefundamentalflexuralresonance,thenodes
3.1.3 elastic modulus [FL ],n—the ratio of stress to strain
are located at 0.224 L from each end, where L is the length of
below the proportional limit.
the specimen.
3.1.4 Poisson’s ratio (µ) [nd],n—the absolute value of the
3.2.7 resonance, n—a slender rod or bar driven into one of
ratio of transverse strain to the corresponding axial strain
the modes of vibration described in 3.2.3 or 3.2.9 is said to be
resulting from uniformly distributed axial stress below the
in resonance when the imposed frequency is such that the
proportional limit of the material.
resultantdisplacementsforagivenamountofdrivingforceare
3.1.4.1 Discussion—In isotropic materialsYoung’s modulus
at a maximum. The resonant frequencies are natural vibration
(E), shear modulus (G), and Poisson’s ratio (µ) are related by
frequencies that are determined by the elastic modulus, mass,
the following equation:
and dimensions of the test specimen.
µ 5 E/2G 2 1
~ !
3.2.8 slender rod or bar, n—in dynamic elastic property
−2
3.1.5 proportional limit [FL ],n—the greatest stress that a
testing, a specimen whose ratio of length to minimum cross-
material is capable of sustaining without deviation from
sectional dimension is at least five and preferably in the range
proportionality of stress to strain (Hooke’s law).
of 20 to 25.
3.2.9 torsional vibrations, n— the vibrations that occur
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
when the oscillations in each cross-sectional plane of a slender
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
rod or bar are such that the plane twists around the length
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. dimension axis.
C1198 − 09 (2013)
4. Summary of Test Method morphology, distribution, orientation, elastic properties, and
interfacial bonding) of the reinforcement/inhomogeneities in
4.1 This test method measures the resonant frequencies of
the specimens will have a direct effect on the elastic properties
test specimens of suitable geometry by exciting them at
of the specimen as a whole. These effects must be considered
continuously variable frequencies. Mechanical excitation of
in interpreting the test results for composites and inhomoge-
the bars is provided through the use of a transducer that
neous materials.
transforms a cyclic electrical signal into a cyclic mechanical
6.1.2 If specific surface treatments (coatings, machining,
forceonthespecimen.Asecondtransducersensestheresulting
grinding, etching, etc.) change the elastic properties of the
mechanical vibrations of the specimen and transforms them
near-surface material, there will be accentuated effects on the
into an electrical signal. The amplitude and frequency of the
properties measured by this flexural method, as compared to
signalaremeasuredbyanoscilloscopeorothermeanstodetect
static/bulk measurements by tensile or compression testing.
resonance. The resonant frequencies, dimensions, and mass of
6.1.3 This test method is not satisfactory for specimens that
the specimen are used to calculate dynamic Young’s modulus
have major discontinuities, such as large cracks (internal or
and dynamic shear modulus.
surface) or voids.
5. Significance and Use
6.2 This test method for determining moduli is limited to
5.1 Thistestmethodmaybeusedformaterialdevelopment,
specimens with regular geometries (rectangular parallelepiped
characterization, design data generation, and quality control
and cylinders) for which analytical equations are available to
purposes. It is specifically appropriate for determining the
relate geometry, mass, and modulus to the resonant vibration
modulus of advanced ceramics that are elastic, homogeneous,
frequencies. This test method is not appropriate for determin-
and isotropic.
ing the elastic properties of materials which cannot be fabri-
5.1.1 This test method is nondestructive in nature. Only
cated into such geometries.
minute stresses are applied to the specimen, thus minimizing
6.2.1 The analytical equations assume parallel/concentric
the possibility of fracture.
dimensions for the regular geometries of the specimen. Devia-
5.1.2 The period of time during which measurement stress
tions from the specified tolerances for the dimensions of the
is applied and removed is of the order of hundreds of
specimens will change the resonant frequencies and introduce
microseconds. With this test method it is feasible to perform
error into the calculations.
measurements at high temperatures, where delayed elastic and
6.2.2 Edge treatments such as chamfers or radii are not
creep effects would invalidate modulus measurements calcu-
considered in the analytical equations. Edge chamfers on
lated from static loading.
flexure bars prepared according to Test Method C1161 will
change the resonant frequency of the test bars and introduce
5.2 This test method has advantages in certain respects over
error into the calculations of the dynamic modulus. It is
the use of static loading systems for measuring moduli in
recommended that specimens for this test not have chamfered
advanced ceramics. It is nondestructive in nature and can be
or rounded edges.Alternately, if narrow rectangular specimens
used for specimens prepared for other tests. Specimens are
with chamfers or edge radii are tested, then the procedures in
subjected to minute strains; hence, the moduli are measured at
Annex A1 should be used to correct the calculated Young’s
or near the origin of the stress-strain curve with the minimum
modulus, E.
possibility of fracture. The period of time during which
6.2.3 For specimens with as-fabricated/rough or uneven
measurement stress is applied and removed is of the order of
surfaces, variations in dimension can have a significant effect
hundreds of microseconds. With this test method it is feasible
in the calculations. For example, in the calculation of the
to perform measurements at high temperatures, where delayed
dynamic modulus, the modulus value is inversely proportional
elastic and creep effects would invalidate modulus measure-
tothecubeofthethickness.Uniformspecimendimensionsand
ments calculated from static loading.
precise measurements are essential for accurate results.
5.3 Thesonicresonantfrequencytechniquecanalsobeused
as a nondestructive evaluation tool for detecting and screening
7. Apparatus
defects (cracks, voids, porosity, density variations) in ceramic
7.1
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.