ASTM C1548-02
(Test Method)Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio of Refractory Materials by Impulse Excitation of Vibration
Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio of Refractory Materials by Impulse Excitation of Vibration
SCOPE
1.1 This test method covers the measurement of the fundamental resonant frequencies for the purpose of calculating the dynamic Young's modulus, the dynamic shear modulus (also known as the modulus of rigidity), and the dynamic Poisson's ratio of refractory materials at ambient temperatures. Specimens of these materials possess specific mechanical resonant frequencies, which are determined by the elastic modulus, mass, and geometry of the test specimen. Therefore, the dynamic elastic properties can be computed if the geometry, mass, and mechanical resonant frequencies of a suitable specimen can be measured. The dynamic Young's modulus is determined using the resonant frequency in the flexural mode of vibration and the dynamic shear modulus is determined using the resonant frequency in the torsional mode of vibration. Poisson's ratio is computed from the dynamic Young's modulus and the dynamic shear modulus.
1.2 Although not specifically described herein, this method can also be performed at high temperatures with suitable equipment modifications and appropriate modifications to the calculations to compensate for thermal expansion.
1.3 The values are stated in SI units and are to be regarded as the standard.
1.4 This standard may involve hazardous materials, operations, and equipment. 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.
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Designation:C1548–02
Standard Test Method for
Dynamic Young’s Modulus, Shear Modulus, and Poisson’s
Ratio of Refractory Materials by Impulse Excitation of
Vibration
This standard is issued under the fixed designation C 1548; 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 dinal, and Torsional Frequencies of Concrete Specimens
C 885 Test Method for Young’s Modulus of Refractory
1.1 This test method covers the measurement of the funda-
Shapes by Sonic Resonance
mental resonant frequencies for the purpose of calculating the
C 1259 Test Method for Dynamic Young’s Modulus, Shear
dynamic Young’s modulus, the dynamic shear modulus (also
Modulus, and Poisson’s Ratio for Advanced Ceramics by
known as the modulus of rigidity), and the dynamic Poisson’s
Impulse Excitation of Vibration
ratio of refractory materials at ambient temperatures. Speci-
mens of these materials possess specific mechanical resonant
3. Summary of Test Method
frequencies, which are determined by the elastic modulus,
3.1 The fundamental resonant frequencies are determined
mass, and geometry of the test specimen. Therefore, the
by measuring the resonant frequency of specimens struck once
dynamic elastic properties can be computed if the geometry,
mechanically with an impacting tool. Frequencies are mea-
mass, and mechanical resonant frequencies of a suitable
sured with a transducer held lightly against the specimen using
specimen can be measured. The dynamic Young’s modulus is
a signal analyzer circuit. Impulse and transducer locations are
determined using the resonant frequency in the flexural mode
selected to induce and measure one of two different modes of
of vibration and the dynamic shear modulus is determined
vibration. The appropriate resonant frequencies, dimensions,
usingtheresonantfrequencyinthetorsionalmodeofvibration.
and mass of each specimen may be used to calculate dynamic
Poisson’s ratio is computed from the dynamic Young’s modu-
Young’s modulus, dynamic shear modulus, and dynamic Pois-
lus and the dynamic shear modulus.
son’s ratio.
1.2 Although not specifically described herein, this method
can also be performed at high temperatures with suitable
4. Significance and Use
equipment modifications and appropriate modifications to the
4.1 This test method is non-destructive and is commonly
calculations to compensate for thermal expansion.
used for material characterization and development, design
1.3 The values are stated in SI units and are to be regarded
data generation, and quality control purposes.The test assumes
as the standard.
that the properties of the specimen are perfectly isotropic,
1.4 This standard may involve hazardous materials, opera-
which may not be true for some refractory materials. The test
tions, and equipment. This standard does not purport to
also assumes that the specimen is homogeneous and elastic.
address all of the safety concerns, if any, associated with its
Specimensthataremicro-crackedaredifficulttotestsincethey
use. It is the responsibility of the user of this standard to
do not yield consistent results. Specimens with low densities
establish appropriate safety and health practices and deter-
have a damping effect and are easily damaged locally at the
mine the applicability of regulatory limitations prior to use.
impactpoint.Insulatingbrickscangenerallybetestedwiththis
technique, but fibrous insulating materials are generally too
2. Referenced Documents
weak and soft to test.
2.1 ASTM Standards:
2 4.2 For quality control use, the test method may be used for
C 71 Terminology Relating to Refractories
measuring only resonant frequencies of any standard size
C 215 Test Method for Fundamental Transverse, Longitu-
specimen.Anelasticmoduluscalculationmaynotbeneededor
even feasible if the shape is non-standard, such as a slide gate
plate containing a hole. Since specimens will vary in both size
This test method is under the jurisdiction of ASTM Committee C08 on
Refractories and is the direct responsibility of Subcommittee C08.01 on Strength.
Current edition approved Nov. 10, 2002. Published July 2003.
2 3
Annual Book of ASTM Standards, Vol 15.01. Annual Book of ASTM Standards, Vol 04.02.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
C1548–02
and mass, acceptable frequencies for each shape and material surface of insulating bricks or other weak materials, plastic or
must be established from statistical data. rubber shapes should be substituted for the steel impactors.
4.3 Dimensional variations can have a significant effect on 5.3 Specimen Support—The support shall permit the speci-
modulus values calculated from the frequency measurements. men to vibrate freely without restricting the desired mode of
Surface grinding may be required to bring some materials into vibration. For room temperature measurements, soft rubber or
the specified tolerance range. plastic strips located at the nodal points are typically used.
4.4 Since cylindrical shapes are not commonly made from Alternately, the specimen can be placed on a thick soft rubber
refractory materials they are not covered by this test method, pad. For elevated temperature measurements, the specimen
but are covered in Test Method C 215. may be suspended from support wires wrapped around the
specimen at nodal points and passing vertically out of the test
5. Apparatus
chamber.
5.1 Electronic System—The electronic system in Fig. 1
6. Test Specimen
consists of a signal conditioner/amplifier, a signal analyzer, a
6.1 Preparation—Test specimens shall be prepared to yield
frequency readout device, and a signal transducer for sensing
uniform rectangular shapes. Normally, brick sized specimens
the vibrations. The system should have sufficient precision to
are used. Although smaller bars cut from bricks are easily
measure frequencies to an accuracy of 0.1 %. Commercial
tested for flexural resonant frequencies, it is more difficult to
instrumentation is available which meets this requirement.
obtain torsional resonance in specimens of square cross-
5.1.1 Frequency Analyzer—This consists of a signal
section. Some pressed brick shapes are dimensionally uniform
conditioner/amplifier to power the transducer and a digital
enough to test without surface grinding, but specimens cut
waveform analyzer or frequency counter with storage capabil-
from larger shapes or prepared by casting or other means often
ity to analyze the signal from the transducer. The waveform
require surface grinding of one or more surfaces to meet the
analyzer shall have a sampling rate of at least 20 000 Hz. The
dimensional criteria noted below.
frequency counter should have an accuracy of 0.1 %.
6.2 Heat Treatment—All specimens shall be prefired to the
5.1.2 Sensor—Apiezeoelectric accelerometer contact trans-
desired temperature and oven dried before testing.
ducer is most commonly used, although non-contact transduc-
6.3 Dimensional Ratios—Specimens having either very
ers based on acoustic, magnetic, or capacitance measurements
small or very large ratios of length to maximum transverse
may also be used. The transducer shall have a frequency
dimensions are frequently difficult to excite in the fundamental
response in the range of 50 Hz to 10 000 Hz, and have a
modes of vibration. Best results are obtained when this ratio is
resonant frequency above 20 000 Hz. The sensor shall have a
between 3 and 5. For use of the equations in this method, the
mark identifying the maximum sensitivity direction so that it
ratio must be at least 2.
can be properly oriented for each vibration mode.
6.4 Dimensional Uniformity—Rectangular specimens shall
5.2 Impactor—Because refractory materials are tested with
have surfaces that are flat and parallel to within 6 0.5 % of the
specimens of various sizes, it is not feasible to specify an
nominal measured value.
impactor with a specific size, weight, or construction method.
6.5 Weight (or Mass) and Dimensions—Determine the
However, hammer style impactors which have light weight
weight (or mass) to the nearest 6 0.5 %. Measure each
handles with the impacting mass concentrated near the end are
dimension to within 6 0.5 %.
preferred to dropping vertical impactors. Steel hammer style
impactors, with head weights between 0.3 and 3 % of the
7. Measurement of Impulse Resonant Frequencies
specimen weight, are recommended. To avoid damaging the
7.1 Transverse Frequency:
7.1.1 Support the specimen so that it may vibrate freely in
thefundamentaltransversemode.Inthismodethenodalpoints
Equipment found suitable is available from J. W. Lemmons, Inc., 3466
(where the displacement is zero) are located at 0.224L from
Bridgeland Drive, Suite 230, St. Louis, MO 63044-260.
FIG. 1 Diagram of Test Apparatus
C1548–02
each end, where Lis the specimen length.Vibrational displace- sensitive pick-up direction coincides with the vibration direc-
ments are a maximum at the ends of the specimen and about tion.InFig.2,thedotonthesensorindicatesthemostsensitive
3/5 maximum at the center. The nodal points are shown in Fig. pickup direction of the sensor and it is pointed upward toward
2 along with recommended impact points and sensor locations. a top-center impact point. The sensor is typically held against
If the specimen does not have a square cross-section, support the specimen with very light hand pressure, but some types
the specimen on its largest face such that it vibrates perpen- could be temporarily attached to large specimens.
dicular to its thinnest dimension. 7.1.4 Select an impact hammer with a head weight 0.3 to
7.1.2 Turn on the electronic system and warm it up accord- 3 %ofthespecimenweightandlightlytapthetopcenterofthe
ing the manufacturers instructions. specimen perpendicular to the surface. Note the reading
7.1.3 Position the sensor on the side face of the specimen at displayed by the electronic system, allow a few seconds for
mid length, with the sensor oriented such that the most existing vibrations to dampen in the specimen, and repeat the
FIG. 2 Impact Points and Transducer Locations
C1548–02
t
procedure at least 3 times until a consistent value is repro-
8.340 ~1 1 0.2023µ 1 2.173µ !
HS S D DJ
L
duced. Record that value and calculate the resonant frequency
t
from it per the manufacturer’s instructions if frequency is not
1.000 1 6.338 1 1 0.1408µ 1 1.536µ !
~
HS S D DJ
L
displayed directly. If a consistent value cannot be obtained,
either the specimen is damaged or other modes of vibration are
interfering with the measurement.
µ = Poisson’s ratio.
7.2 Torsional Frequency
8.1.1.1 If L / t$ 20, T can be simplified to:
7.2.1 Support the specimen so that it may vibrate freely in
t
torsion. In this mode there is a single nodal point at the center
T 5 1.000 1 6.585
S S D D
L
and vibrations are a maximum at the ends. The impact and
and E can be calculated directly.
sensor pickup points are located at 0.224L from the ends. This
8.1.1.2 If L / t < 20, then an initial Poisson’s ratio must be
location is a nodal point for flexural vibration and minimizes
assumed to start the computations.An iterative process is then
interference from flexural vibrations.
used to determine a value of Poisson’s ratio, based on
7.2.2 Turn on the electronic system and warm it up accord-
experimental Young’s modulus and shear modulus. This itera-
ing to the manufacturers instructions.
tive process is shown in Fig. 3 and described below.
7.2.3 Position the sensor on the side face of the specimen at
(1) Determine the fundamental flexural and torsional reso-
0.224L, with the sensor oriented such that the sensitive pick-up
nant frequencies of the rectangular test specimen. Using Eq 2,
direction coincides with the vibration direction. In Fig. 2, the
the dynamic shear modulus of the test specimen is calculated
dot on the sensor indicates the most sensitive pickup direction
from the fundamental torsional resonant frequency and the
of the sensor and it is pointed upward toward a top impact
dimension and mass of the specimen.
point.
(2) Using Eq 1, the dynamic Young’s modulus of the
7.2.4 Select an impact hammer with a head weight 0.3 to
rectangular test specimen is calculated from the fundamental
3 % of the specimen weight and lightly tap the top of the
flexural resonant frequency, the dimensions and mass of the
specimen at a 0.224L location perpendicular to the surface.
specimen, and the initial/iterative Poisson’s ratio.
Note the reading displayed by the electronic system, allow a
(3) The dynamic shear modulus and Young’s values
few seconds for existing vibrations to dissipate, and repeat the
modulus.calculated in steps (1) and (2) are substituted into Eq
process at least 3 times until a consistent value is reproduced.
3, for Poisson’s ratio. A new value for Poisson’s ratio is then
Record that value and calculate the resonant frequency from it
calculated for another iteration starting at step (2).
if frequency is not displayed directly.
(4) Steps (2) and (3) are repeated until no significant
8. Calculations difference (2 % or less) is observed between the last iterative
,
5 6 value and the final computed value of the Poisson’s ratio.
8.1 Dynamic Young’s Modulus :
Self-consistent values for the moduli are thus obtained.
8.1.1 From the fundamental flexural vibration of a rectan-
7,8
8.2 Dynamic Shear Modulus :
gular bar:
8.2.1 From the fundamental torsional vibration of a rectan-
2 3
mf L
f
gular bar:
E 5 0.9465 T (1)
S DS 3D 1
b
t
4Lmf B
~ !
t
G 5 (2)
H JH J
~bt! ~1 1A!
where:
E = Young’s modulus, Pa,
where:
m = mass of the bar, g,
G = shear modulus, Pa, and
b = width of the bar, mm,
f = fundamental resonant frequency of the bar in torsion,
t
L = length of the bar, mm,
Hz.
t = thickness of the bar, mm,
f = fundamental resonant frequency of the bar in flexure,
b t
f
HS D S DJ
Hz, and t b
B 5
2 6
T = correction factor for fundamental flexural made to
t t t
4 2 2.52 1 0.21
H S D S D S D J
accountforfinitethicknessofbar,Poisson’sratio,etc. b b b
2 3
b b b
0.5062 2 0.8776 1 0.3504 2 0.0078
H S D S D S D J
2 t t t
t t
A 5
T 5 1 1 6.585 1 1 0.0752µ 1 0.8109µ 2 0.868 2
~ ! 2
1 S D S D
b b
L L
12.03 1 9.892
H S D S D J
t t
Spinner, S., Reichard, T. W., and Tefft, W. E., “AComparison of Experimental
and Theoretical Relations Between Young’s Modulus and the Flexural and Longi- Pickett, G., “Equations for Computing Elastic Constants from Flexural and
tudinal Resonance F
...
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