ASTM C1198-09
(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 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). 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 f...
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Designation: C1198 − 09
StandardTest 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—Corrections were made to the 2008 version and the year date was changed on Nov. 4, 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-
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
2
ceramics that are elastic, homogeneous, and isotropic (3).
advent of computers and sophisticated hand calculators, the
actual formulas can be easily used and provide greater accu-
1 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 Nov. 4, 2009. Published November 2009. Originally
ϵ1
approved in 1991. Last previous edition approved in 2008 as C1198–08 . DOI: only.
10.1520/C1198-09.
2 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
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