ASTM C1548-02(2012)

Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio of Refractory Materials by Impulse Excitation of Vibration

SIGNIFICANCE AND USE
This test method is non-destructive and is commonly used for material characterization and development, design data generation, and quality control purposes. The test assumes that the properties of the specimen are perfectly isotropic, which may not be true for some refractory materials. The test also assumes that the specimen is homogeneous and elastic. Specimens that are micro-cracked are difficult to test since they do not yield consistent results. Specimens with low densities have a damping effect and are easily damaged locally at the impact point. Insulating bricks can generally be tested with this technique, but fibrous insulating materials are generally too weak and soft to test.
For quality control use, the test method may be used for measuring only resonant frequencies of any standard size specimen. An elastic modulus calculation may not be needed or even feasible if the shape is non-standard, such as a slide gate plate containing a hole. Since specimens will vary in both size and mass, acceptable frequencies for each shape and material must be established from statistical data.
Dimensional variations can have a significant effect on modulus values calculated from the frequency measurements. Surface grinding may be required to bring some materials into the specified tolerance range.  
Since cylindrical shapes are not commonly made from refractory materials they are not covered by this test method, but are covered in Test Method C215.
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.

General Information

• Status: Historical
• Publication Date: 29-Feb-2012
• ICS: 81.080 - Refractories
• Technical Committee: C08 - Refractories
• Drafting Committee: C08.01 - Strength

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: C1548 − 02 (Reapproved 2012)
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 C1548; 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 (´) indicates an editorial change since the last revision or reapproval.
1. Scope 2. Referenced Documents
2.1 ASTM Standards:
1.1 This test method covers the measurement of the funda-
C71 Terminology Relating to Refractories
mental resonant frequencies for the purpose of calculating the
C215 Test Method for Fundamental Transverse,
dynamic Young’s modulus, the dynamic shear modulus (also
Longitudinal, and Torsional Resonant Frequencies of
known as the modulus of rigidity), and the dynamic Poisson’s
Concrete Specimens
ratio of refractory materials at ambient temperatures. Speci-
C885 Test Method for Young’s Modulus of Refractory
mens of these materials possess specific mechanical resonant
Shapes by Sonic Resonance
frequencies, which are determined by the elastic modulus,
C1259 Test Method for Dynamic Young’s Modulus, Shear
mass, and geometry of the test specimen. Therefore, the
Modulus, and Poisson’s Ratio for Advanced Ceramics by
dynamic elastic properties can be computed if the geometry,
Impulse Excitation of Vibration
mass, and mechanical resonant frequencies of a suitable
specimen can be measured. The dynamic Young’s modulus is
3. Summary of Test Method
determined using the resonant frequency in the flexural mode
3.1 The fundamental resonant frequencies are determined
of vibration and the dynamic shear modulus is determined
by measuring the resonant frequency of specimens struck once
usingtheresonantfrequencyinthetorsionalmodeofvibration.
mechanically with an impacting tool. Frequencies are mea-
Poisson’s ratio is computed from the dynamic Young’s modu-
sured with a transducer held lightly against the specimen using
lus and the dynamic shear modulus.
a signal analyzer circuit. Impulse and transducer locations are
1.2 Although not specifically described herein, this method
selected to induce and measure one of two different modes of
can also be performed at high temperatures with suitable
vibration. The appropriate resonant frequencies, dimensions,
equipment modifications and appropriate modifications to the
and mass of each specimen may be used to calculate dynamic
calculations to compensate for thermal expansion.
Young’s modulus, dynamic shear modulus, and dynamic Pois-
son’s ratio.
1.3 The values are stated in SI units and are to be regarded
as the standard.
4. Significance and Use
1.4 This standard may involve hazardous materials,
4.1 This test method is non-destructive and is commonly
operations, and equipment. This standard does not purport to
used for material characterization and development, design
address all of the safety concerns, if any, associated with its
data generation, and quality control purposes.The test assumes
use. It is the responsibility of the user of this standard to
that the properties of the specimen are perfectly isotropic,
establish appropriate safety and health practices and deter-
which may not be true for some refractory materials. The test
mine the applicability of regulatory limitations prior to use.
also assumes that the specimen is homogeneous and elastic.
Specimensthataremicro-crackedaredifficulttotestsincethey
do not yield consistent results. Specimens with low densities
This test method is under the jurisdiction of ASTM Committee C08 on
Refractories and is the direct responsibility of Subcommittee C08.01 on Strength. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved March 1, 2012. Published April 2012. Originally contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
approved in 2002. Last previous edition approved in 2007 as C1548 – 02 (2007). Standards volume information, refer to the standard’s Document Summary page on
DOI: 10.1520/C1548-02R12. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
C1548 − 02 (2012)
FIG. 1 Diagram of Test Apparatus
have a damping effect and are easily damaged locally at the mark identifying the maximum sensitivity direction so that it
impactpoint.Insulatingbrickscangenerallybetestedwiththis can be properly oriented for each vibration mode.
technique, but fibrous insulating materials are generally too
5.2 Impactor—Because refractory materials are tested with
weak and soft to test.
specimens of various sizes, it is not feasible to specify an
4.2 For quality control use, the test method may be used for impactor with a specific size, weight, or construction method.
measuring only resonant frequencies of any standard size However, hammer style impactors which have light weight
specimen.Anelasticmoduluscalculationmaynotbeneededor handles with the impacting mass concentrated near the end are
even feasible if the shape is non-standard, such as a slide gate preferred to dropping vertical impactors. Steel hammer style
plate containing a hole. Since specimens will vary in both size impactors, with head weights between 0.3 and 3 % of the
and mass, acceptable frequencies for each shape and material specimen weight, are recommended. To avoid damaging the
must be established from statistical data. surface of insulating bricks or other weak materials, plastic or
rubber shapes should be substituted for the steel impactors.
4.3 Dimensional variations can have a significant effect on
modulus values calculated from the frequency measurements. 5.3 Specimen Support—The support shall permit the speci-
Surface grinding may be required to bring some materials into men to vibrate freely without restricting the desired mode of
the specified tolerance range. vibration. For room temperature measurements, soft rubber or
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 C215.
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
consists of a signal conditioner/amplifier, a signal analyzer, a
6. Test Specimen
frequency readout device, and a signal transducer for sensing
6.1 Preparation—Test specimens shall be prepared to yield
the vibrations. The system should have sufficient precision to
uniform rectangular shapes. Normally, brick sized specimens
measure frequencies to an accuracy of 0.1 %. Commercial
are used. Although smaller bars cut from bricks are easily
instrumentation is available which meets this requirement.
tested for flexural resonant frequencies, it is more difficult to
5.1.1 Frequency Analyzer—This consists of a signal
obtain torsional resonance in specimens of square cross-
conditioner/amplifier to power the transducer and a digital
section. Some pressed brick shapes are dimensionally uniform
waveform analyzer or frequency counter with storage capabil-
enough to test without surface grinding, but specimens cut
ity to analyze the signal from the transducer. The waveform
from larger shapes or prepared by casting or other means often
analyzer shall have a sampling rate of at least 20 000 Hz. The
require surface grinding of one or more surfaces to meet the
frequency counter should have an accuracy of 0.1 %.
dimensional criteria noted below.
5.1.2 Sensor—Apiezeoelectric accelerometer contact trans-
ducer is most commonly used, although non-contact transduc-
6.2 Heat Treatment—All specimens shall be prefired to the
ers based on acoustic, magnetic, or capacitance measurements
desired temperature and oven dried before testing.
may also be used. The transducer shall have a frequency
6.3 Dimensional Ratios—Specimens having either very
response in the range of 50 Hz to 10 000 Hz, and have a
small or very large ratios of length to maximum transverse
resonant frequency above 20 000 Hz. The sensor shall have a
dimensions are frequently difficult to excite in the fundamental
modes of vibration. Best results are obtained when this ratio is
between 3 and 5. For use of the equations in this method, the
Equipment found suitable is available from J. W. Lemmons, Inc., 3466
Bridgeland Drive, Suite 230, St. Louis, MO 63044-260. ratio must be at least 2.
C1548 − 02 (2012)
6.4 Dimensional Uniformity—Rectangular specimens shall dot on the sensor indicates the most sensitive pickup direction
have surfaces that are flat and parallel to within 60.5 % of the of the sensor and it is pointed upward toward a top impact
nominal measured value. point.
7.2.4 Select an impact hammer with a head weight 0.3 to
6.5 Weight (or Mass) and Dimensions—Determine the
3 % of the specimen weight and lightly tap the top of the
weight (or mass) to the nearest 60.5 %. Measure each dimen-
specimen at a 0.224L location perpendicular to the surface.
sion to within 60.5 %.
Note the reading displayed by the electronic system, allow a
few seconds for existing vibrations to dissipate, and repeat the
7. Measurement of Impulse Resonant Frequencies
process at least 3 times until a consistent value is reproduced.
7.1 Transverse Frequency:
Record that value and calculate the resonant frequency from it
7.1.1 Support the specimen so that it may vibrate freely in
if frequency is not displayed directly.
thefundamentaltransversemode.Inthismodethenodalpoints
(where the displacement is zero) are located at 0.224L from 8. Calculations
each end, where Lis the specimen length.Vibrational displace- 4,5
8.1 Dynamic Young’s Modulus:
ments are a maximum at the ends of the specimen and about
8.1.1 From the fundamental flexural vibration of a rectan-
3/5 maximum at the center. The nodal points are shown in Fig.
gular bar:
2 along with recommended impact points and sensor locations.
2 3
mf L
f
If the specimen does not have a square cross-section, support
E 5 0.9465 T (1)
S DS 3D
b t
the specimen on its largest face such that it vibrates perpen-
dicular to its thinnest dimension.
where:
7.1.2 Turn on the electronic system and warm it up accord-
E = Young’s modulus, Pa,
ing the manufacturers instructions.
m = mass of the bar, g,
7.1.3 Position the sensor on the side face of the specimen at b = width of the bar, mm,
mid length, with the sensor oriented such that the most L = length of the bar, mm,
t = thickness of the bar, mm,
sensitive pick-up direction coincides with the vibration direc-
f = fundamental resonant frequency of the bar in flexure,
tion.InFig.2,thedotonthesensorindicatesthemostsensitive
f
Hz, and
pickup direction of the sensor and it is pointed upward toward
T = correction factor for fundamental flexural made to
a top-center impact point. The sensor is typically held against 1
account for finite thickness of bar, Poisson’s ratio, etc.
the specimen with very light hand pressure, but some types
could be temporarily attached to large specimens.
7.1.4 Select an impact hammer with a head weight 0.3 to 2
t t
T 5 116.585 ~110.0752µ10.8109µ ! 2 0.868 2
S D S D
3 %ofthespecimenweightandlightlytapthetopcenterofthe 1
L L
specimen perpendicular to the surface. Note the reading 4
t
8.340 110.2023µ12.173µ
HS ~ ! S D DJ
displayed by the electronic system, allow a few seconds for
L
existing vibrations to dampen in the specimen, and repeat the 2
t
1.00016.338 110.1408µ11.536µ
HS ~ ! S D DJ
procedure at least 3 times until a consistent value is repro-
L
duced. Record that value and calculate the resonant frequency
µ = Poisson’s ratio.
from it per the manufacturer’s instructions if frequency is not
displayed directly. If a consistent value cannot be obtained,
8.1.1.1 If L / t ≥ 20, T can be simplified to:
either the specimen is damaged or other modes of vibration are
t
interfering with the measurement.
T 5 1.00016.585
S S D D
L
7.2 Torsional Frequency
and E can be calculated directly.
7.2.1 Support the specimen so that it may vibrate freely in
8.1.1.2 If L / t < 20, then an initial Poisson’s ratio must be
torsion. In this mode there is a single nodal point at the center
assumed to start the computations.An iterative process is then
and vibrations are a maximum at the ends. The impact and
sensor pickup points are located at 0.224L from the ends. This
location is a nodal point for flexural vibration and minimizes
Spinner, S., Reichard, T. W., and Tefft, W. E., “AComparison of Experimental
interference from flexural vibrations.
and Theoretical Relations Between Young’s Modulus and the Flexural and Longi-
7.2.2 Turn on the electronic system and warm it up accord-
tudinal Resonance Frequencies of Uniform Bars,” Journal of Research of the
National Bureau of Standards—A. Physics and Chemistry, Vol 64A, No. 2,
ing to the manufacturers instructions.
March-April, 1960.
7.2.3 Position the sensor on the side face of the specimen at
Spinner, S., and Tefft, W. E., “A Method for Determining Mechanical
0.224L, with the sensor oriented such that the sensitive pick-up
ResonanceFrequenciesandforCalculatingElasticModulifromtheseFrequencies,”
direction coincides with the vibration direction. In Fig. 2, the Proceedings, ASTM, 1961, pp. 1221-1238.
C1548 − 02 (2012)
FIG. 2 Impact Points and Transducer Locations
used to determine a value of Poisson’s ratio, based on experi- (2) Using Eq 1, the dynamic Young’s modulus of the
mental Young’s modulus and shear modulus. This iterative rectangular test specimen is calculated from the fundamental
process is shown in Fig. 3 and described below. flexural resonant frequency, the dimensions and mass of the
(1) Determine the fundamental flexural and torsional reso- specimen, and the initial/iterative Poisson’s ratio.
nant frequencies of the rectangular test specimen. Using Eq 2, (3) The dynamic shear modulus andYoung’s values modu-
the dynamic shear modulus of the test specimen is calculated lus.calculated in steps (1) and (2) are substituted into Eq 3, for
from the fundamental torsional resonant frequency and the Poisson’s ratio. A new value for Poisson’s ratio is then
dimension and mass of the specimen. calculated for another iteration starting at step (2).
C1548 − 02 (2012)
FIG. 3 Flow Chart for
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