ASTM C1198-08e1
(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
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.
This test method is nondestructive in nature. Only minute stresses are applied to the specimen, thus minimizing the 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.
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.
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 E 2001 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 (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 ...
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´1
Designation:C1198–08
Standard Test Method for
Dynamic Young’s Modulus, Shear Modulus, and Poisson’s
1
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
´ NOTE—Paragraph 10.1.2 was editorially updated in May 2009.
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-
1.4 A high-temperature furnace and cryogenic cabinet are
tions. Dynamic Young’s modulus and dynamic shear modulus
described for measuring the dynamic elastic moduli as a
are used to compute Poisson’s ratio.
function of temperature from −195 to 1200°C.
1.2 This test method measures the resonant frequencies of
1.5 Modification of this test method for use in quality
test specimens of suitable geometry by mechanically exciting
control is possible.Arange of acceptable resonant frequencies
them at continuously variable frequencies. Mechanical excita-
is determined for a specimen with a particular geometry and
tionofthebarsisprovidedthroughtheuseofatransducerthat
mass.Any specimen with a frequency response falling outside
transforms a cyclic electrical signal into a cyclic mechanical
this frequency range is rejected. The actual modulus of each
forceonthespecimen.Asecondtransducersensestheresulting
specimen need not be determined as long as the limits of the
mechanical vibrations of the specimen and transforms them
selected frequency range are known to include the resonant
into an electrical signal. The amplitude and frequency of the
frequency that the specimen must possess if its geometry and
signalaremeasuredbyanoscilloscopeorothermeanstodetect
mass are within specified tolerances.
resonant vibration in the desired mode. The resonant frequen-
1.6 The procedures in this test method are, where possible,
cies, dimensions, and mass of the specimen are used to
consistent with the procedures of Test Methods C623, C747,
calculate dynamicYoung’s modulus and dynamic shear modu-
and C848.The tables of these test methods have been replaced
lus. (See Fig. 1)
by the actual formulas from the original references. With the
1.3 Thistestmethodisspecificallyappropriateforadvanced
2 advent of computers and sophisticated hand calculators, the
ceramics that are elastic, homogeneous, and isotropic (1).
actual formulas can be easily used and provide greater accu-
racy than factor tables.
1
This test method is under the jurisdiction of ASTM Committee C28 on
1.7 The values stated in SI units are to be regarded as the
Advanced Ceramics and is the direct responsibility of Subcommittee C28.01 on
standard. The values given in parentheses are for information
Mechanical Properties and Performance.
only.
Current edition approved Jan. 1, 2008. Published January 2008. Originally
approved in 1991. Last previous edition approved in 2001 as C1198–01. DOI:
10.1520/C1198-08E01.
2
The boldface numbers given in parentheses refer to a list of references at the
end of the text.
Copyright ©ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA19428-2959, United States.
1
---------------------- Page: 1 ----------------------
NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Please contact ASTM International (www.as
...
This document is not anASTM standard and is intended only to provide the user of anASTM 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.
´1
Designation:C 1198–01 Designation:C 1198–08
Standard Test Method for
Dynamic Young’s Modulus, Shear Modulus, and Poisson’s
1
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.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1
´ NOTE—Paragraph 10.1.2 was editorially updated in May 2009.
1. 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. DynamicYoung’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.
1.2This test method is specifically appropriate for advanced ceramics that are elastic, homogeneous, and isotropic
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
byanoscilloscopeorothermeanstodetectresonantvibrationinthedesiredmode.Theresonantfrequencies,dimensions,andmass
of the specimen are used to calculate dynamic Young’s modulus and dynamic shear modulus. (See Fig. 1)
2
1.3 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
mustbeconsideredininterpretingthetestresultsforcomposites.Thistestmethodisnotsatisfactoryforspecimensthathavecracks
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.
1.3A1.4 Ahigh-temperaturefurnaceandcryogeniccabinetaredescribedformeasuringthedynamicelasticmoduliasafunction
of temperature from −195 to 1200°C.
1.45 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.
1.5The1.6 Theproceduresinthistestmethodare,wherepossible,consistentwiththeproceduresofTestMethodsC623,C747,
andC848.Thetablesofthesetestmethodshavebeenreplacedbytheactualformulasfromtheoriginalreferences.Withtheadvent
of computers and sophisticated hand calculators, the actual formulas can be easily used and provide greater accuracy than factor
tables.
1.6The1.7 The values stated in SI units are to be regarded as the standard. The values given in parentheses are for information
only.
1.71.8 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.
1
This test method is under the jurisdiction of ASTM Committee C28 on Advanced Ceramics and is the direct r
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