ASTM C885-87(2020)
(Test Method)Standard Test Method for Young’s Modulus of Refractory Shapes by Sonic Resonance
Standard Test Method for Young’s Modulus of Refractory Shapes by Sonic Resonance
SIGNIFICANCE AND USE
4.1 Young’s modulus is a fundamental mechanical property of a material.
4.2 This test method is used to determine the dynamic modulus of elasticity of rectangular shapes. Since the test is nondestructive, specimens may be used for other tests as desired.
4.3 This test method is useful for research and development, engineering application and design, manufacturing process control, and for developing purchasing specifications.
4.4 The fundamental assumption inherent in this test method is that a Poisson’s ratio of 1/6 is typical for heterogeneous refractory materials. The actual Poisson's ratio may differ.
SCOPE
1.1 This test method covers a procedure for measuring the resonance frequency in the flexural (transverse) mode of vibration of rectangular refractory brick or rectangularly shaped monoliths at room temperature. Young's modulus is calculated from the resonance frequency of the shape, its mass (weight), and dimensions.
1.2 Units—The values stated in inch-pound units are to be regarded as standard. The values given in parentheses are mathematical conversions to SI units that are provided for information only and are not considered standard.
1.2.1 Although the Hertz (Hz) is an SI unit, it is derived from seconds which is also an inch-pound unit.
1.3 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, health, and environmental practices and determine the applicability of regulatory limitations prior to use.
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
General Information
Relations
Standards Content (Sample)
This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: C885 − 87 (Reapproved 2020)
Standard Test Method for
Young’s Modulus of Refractory Shapes by Sonic
Resonance
This standard is issued under the fixed designation C885; 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 C623 Test Method for Young’s Modulus, Shear Modulus,
and Poisson’s Ratio for Glass and Glass-Ceramics by
1.1 This test method covers a procedure for measuring the
Resonance
resonance frequency in the flexural (transverse) mode of
C747 Test Method for Moduli of Elasticity and Fundamental
vibration of rectangular refractory brick or rectangularly
Frequencies of Carbon and Graphite Materials by Sonic
shaped monoliths at room temperature. Young’s modulus is
Resonance
calculated from the resonance frequency of the shape, its mass
C848 Test Method for Young’s Modulus, Shear Modulus,
(weight), and dimensions.
and Poisson’s Ratio For Ceramic Whitewares by Reso-
1.2 Units—The values stated in inch-pound units are to be
nance
regarded as standard. The values given in parentheses are
mathematical conversions to SI units that are provided for
3. Summary of Test Method
information only and are not considered standard.
3.1 Test specimens are vibrated in flexure over a broad
1.2.1 Although the Hertz (Hz) is an SI unit, it is derived
frequencyrange;mechanicalexcitationisprovidedthroughthe
from seconds which is also an inch-pound unit.
use of a vibrating driver that transforms an initial electrical
1.3 This standard does not purport to address all of the
signal into a mechanical vibration. A detector senses the
safety concerns, if any, associated with its use. It is the
resultingmechanicalvibrationsofthespecimenandtransforms
responsibility of the user of this standard to establish appro-
them into an electrical signal that can be displayed on the
priate safety, health, and environmental practices and deter-
screen of an oscilloscope to detect resonance by a Lissajous
mine the applicability of regulatory limitations prior to use.
figure.The calculation ofYoung’s modulus from the resonance
1.4 This international standard was developed in accor-
frequency measured is simplified by assuming that Poisson’s
dance with internationally recognized principles on standard-
ratio is ⁄6 for all refractory materials.
ization established in the Decision on Principles for the
Development of International Standards, Guides and Recom-
4. Significance and Use
mendations issued by the World Trade Organization Technical
4.1 Young’s modulus is a fundamental mechanical property
Barriers to Trade (TBT) Committee.
of a material.
2. Referenced Documents
4.2 This test method is used to determine the dynamic
modulus of elasticity of rectangular shapes. Since the test is
2.1 ASTM Standards:
nondestructive, specimens may be used for other tests as
C134 Test Methods for Size, Dimensional Measurements,
desired.
and Bulk Density of Refractory Brick and Insulating
Firebrick
4.3 Thistestmethodisusefulforresearchanddevelopment,
C215 Test Method for Fundamental Transverse,
engineering application and design, manufacturing process
Longitudinal, and Torsional Resonant Frequencies of
control, and for developing purchasing specifications.
Concrete Specimens
4.4 The fundamental assumption inherent in this test
method is that a Poisson’s ratio of ⁄6 is typical for heteroge-
This test method is under the jurisdiction of ASTM Committee C08 on neous refractory materials. The actual Poisson’s ratio may
Refractories and is the direct responsibility of Subcommittee C08.01 on Strength.
differ.
Current edition approved Sept. 1, 2020. Published September 2020. Originally
approved in 1978. Last previous edition approved in 2012 as C885 – 87 (2012).
5. Apparatus
DOI: 10.1520/C0885-87R20.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
5.1 A block diagram of a suggested test apparatus arrange-
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
ment is shown in Fig. 1. Details of the equipment are as
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. follows:
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
C885 − 87 (2020)
FIG. 1 Block Diagram of Apparatus
5.1.1 Audio Oscillator, having a continuously variable, cali- 6. Sampling and Specimen Preparation
brated frequency output from about 50 Hz to at least 10 kHz.
6.1 Specimensmustberectangularprisms.Theymaybefull
5.1.2 Audio Amplifier, having a power output sufficient to
straight brick or rectangular samples cut from brick shapes,
ensure that the type of driver used can excite the specimen; the
rectangular straight shapes of monolithic refractories, or rect-
output of the amplifier must be adjustable.
angularspecimenscutfrommonolithicshapes.Forbestresults,
5.1.3 Driver, which may consist of a transducer or a
their length to thickness ratio should be at least 3 to 1.
loudspeaker from which the cone has been removed and
Maximumspecimensizeandmassareprimarilydeterminedby
replaced with a probe (connecting rod) oriented parallel to the
the test system’s energy capability and by the resonance
direction of the vibration; suitable vibration-isolating mounts.
response characteristics of the material. Minimum specimen
size and mass are primarily determined by adequate and
NOTE 1—For small specimens, an air column may preferably be used
for “coupling” the loudspeaker to the specimen.
optimum coupling of the driver and the detector to the
specimen, and by the resonance response characteristics of the
5.1.4 Detector, which may be a transducer or a balance-
material. Measure the mass (weight) and dimensions of the dry
mounted monaural (crystal or magnetic) phonograph pick-up
specimens in accordance with Test Methods C134 and record.
cartridge of good frequency response; the detector should be
movable across the specimen; suitable vibration-isolating
7. Procedure
mounts.
5.1.5 Pre-Scope Amplifier in the detector circuit, 7.1 Refractories can vary markedly in their response to the
impedance-matched with the detector used; the output must be driver’s frequency; the geometry of the specimens also plays a
adjustable. significant role in their response characteristics. Variations in
the following procedure are permissible as long as flexural and
5.1.6 Indicating Devices, including an oscilloscope, a reso-
nance indicator (voltmeter or ammeter), and a frequency fundamental resonance are verified (Notes 6 and 7). Fig. 2 and
indicator, which may be the control dial of the audio-oscillator
(accurately readable to 630 Hz or better) or, preferably, a
frequency meter, for example, a digital frequency counter.
5.1.7 Specimen Support, consisting of two knife edges (can
be steel, rubber-coated steel, or medium-hard rubber) of a
length at least equal to the width of the specimens; the distance
between the knife edges must be adjustable.
NOTE 2—The support for the knife edges may be a foam rubber pad,
and should be vibration-isolated from drive and detector supports.
NOTE 3—Alternatively, knife edges can be omitted and the specimen
may be placed directly on a foam rubber pad if the test material is easily FIG. 2 Typical Specimen Positioning for Measurement of Flexural
excitable due to its composition and geometry. Resonance
C885 − 87 (2020)
Fig. 3 illustrate a typical specimen positioning and the desired at which the signal amplitude is maximized. Adjust the
mode of vibration, respectively. oscilloscope so that a sharply defined horizontal baseline exists
when the specimen is not excited. Scan frequency with the
7.2 Sample Placement—Place the specimen “flat” (thick-
audio oscillator until fundamental flexural specimen resonance
ness dimension perpendicular to supports) on parallel knife
is indicated by an oval to circular Lissajous figure at the
edges at 0.224 l (where l is the length of the specimen) from its
oscilloscope and maximum output is shown at the resonance
ends. Optionally, the specimen can be placed on a foam rubber
indicator. Record the resonance frequency.
pad.
NOTE 6—To verify the flexural mode of vibration, move the detector to
7.3 Driver Placement—Place the driver preferably at the
the top center of the specimen. The oval or circular oscilloscope pattern
center of the top or bottom face of the specimen using
shall be maintained. Placement of the detector above the nodal points (at
moderate balanced pressure or spring action.
0.224 l) shall cause a Lissajous pattern and high output at the resonance
indicator to disappear.
NOTE 4—Especially with small (thin) specimens, the lightest possible
NOTE 7—To verify the fundamental mode of flexural resonance, excite
driver pressure to ensure adequate “coupling” must be used in order to
the specimen at one half of the frequency established in 7.5. A “figure
achieve proper resonance response. In small specimens, exact placement
eight” Lissajous pattern should appear at the oscilloscope when the
of the driver at the very center of the flat specimen is important; also, an
detector is placed at the end center or at the top center of the specimen.
air column may be used for “coupling.”
7.4 Detector Placement—Place the detector preferably at
8. Calculation
one end of the specimen and at the center of either the width or
8.1 Data determined on individual specimens include:
thickness (considering the orientation of maximum response of
8.1.1 l = length of specimen, in.,
the detector) using minimal pressure.
8.1.2 b = width of specimen, in.,
NOTE5—Makesurethatthestylusofthephonographcartridge(ifused) 8.1.3 t = thickness of specimen, in.,
is well secured.
8.1.4 w = mass (weight) of specimen, lb, and
8.1.5 f = fundamental flexural resonance frequency, Hz.
7.5 Activate and warm up the equipment so that power
adequate to excite the specimen is delivered to the driver. Set
8.2 CalculateYoung’s modulus E, in psi, of the specimen as
the gain on the detector circuit high enough to detect vibration
follows:
in the specimen, and to display it on the oscilloscope screen
E 5 C ·w·f (1)
with sufficient amplitude to measure accurately the frequency
2 2
where C =[C b]/b (in s /in. ) is calculated from values of
1 1
[C b] listed in Table 1 for various l/t ratios based on Pickett’s
equationssolvedforaPoisson’sratioof ⁄6.Alternatively,[C b]
can be computed directly from l and t using Pickett’s original
equations and correction factors, as described in Appendix X1.
Pickett, G., “Equations for Computing Elastic Constants from Flexural and
Torsional Resonant Frequencies of Vibration of Prisms and Cylinders,”
FIG. 3 Fundamental Mode of Vibration in Flexure (Side View) Proceedings, ASTM, Vol 45, 1945, pp. 846–863.
TABLE 1 [C b] Values
l/t [C b] l/t [C b] l/t [C b] l/t [C b] l/t [C b] l/t [C b]
1 1 1 1 1 1
2.50 0.0750 3.10 0.1200 3.70 0.1815 4.30 0.2627 4.90 0.3665 5.50 0.4963
2.51 0.0756 3.11 0.1209 3.71 0.1827 4.31 0.2642 4.91 0.3685 5.51 0.4988
2.52 0.0763 3.12 0.1218 3.72 0.1839 4.32 0.2657 4.92 0.3704 5.52 0.5012
2.53 0.0769 3.13 0.1227 3.73 0.1851 4.33 0.2673 4.93 0.3724 5.53 0.5036
2.54 0.0776 3.14 0.1236 3.74 0.1863 4.34 0.2688 4.94 0.3743 5.54 0.5060
2.55 0.0782 3.15 0.1245 3.75 0.1875 4.35 0.2704 4.95 0.3763 5.55 0.5084
2.56 0.0789 3.16 0.1254 3.76 0.1887 4.36 0.2720 4.96 0.3783 5.56 0.5109
2.57 0.0795 3.17 0.1263 3.77 0.1899 4.37 0.2735 4.97 0.3803 5.57 0.5133
2.58 0.0802 3.18 0.1272 3.78 0.1911 4.38 0.2751 4.98 0.3823 5.58 0.5158
2.59 0.0808 3.19 0.1281 3.79 0.1924 4.39 0.2767 4.99 0.3843 5.59 0.5183
2.60 0.0815 3.20 0.1291 3.80 0.1936 4.40 0.2783 5.00 0.3863 5.60 0.5207
2.61 0.0822 3.21 0.1300 3.81 0.1948 4.41 0.2799 5.01 0.3883 5.61 0.5232
2.62 0.0828 3.22 0.1309 3.82 0.1961 4.42 0.2815 5.02 0.3903 5.62 0.5257
2.63 0.0835 3.23 0.1318 3.83 0.1973 4.43 0.2831 5.03 0.3924 5.63 0.5282
2.64 0.0842 3.24 0.1328 3.84 0.1986 4.44 0.2847 5.04 0.3944 5.64 0.5307
2.65 0.0849 3.25 0.1337 3.85 0.1999 4.45 0.2864 5.05 0.3964 5.65 0.5332
2.66 0.0856 3.26 0.1347 3.86 0.2011 4.46 0.2880 5.06 0.3985 5.66 0.5358
2.67 0.0863 3.27 0.1356 3.87 0.2024 4.47 0.2896 5.07 0.4005 5.67 0.5383
2.68 0.0870 3.28 0.1366 3.88 0.2037 4.48 0.2913 5.08 0.4026 5.68 0.5408
2.69 0.0877 3.29 0.1376 3.89 0.2050 4.49 0.2929 5.09 0.4047 5.69 0.5434
2.70 0.0884 3.30 0.1385 3.90 0.2062 4.50 0.2946 5.10 0.4068 5.70 0.5459
2.71 0.0891 3.31 0.1395 3.91 0.2075 4.51 0.2963 5.11 0.4089 5.71 0.5485
2.72 0.0898 3.32 0.1405 3.92 0.2088 4.52 0.2979 5.12 0.4110 5.72 0.5511
C885 − 87 (2020)
TABLE 1 Continued
l/t [C b] l/t [C b] l/t [C b] l/t [C b] l/t [C b] l/t [C b]
1 1 1 1 1 1
2.73 0.0905 3.33 0.1415 3.93 0.2101 4.53 0.2996 5.13 0.4131 5.73 0.5537
2.74 0.0912 3.34 0.1425 3.94 0.2115 4.54 0.3013 5.14 0.4152 5.74 0.5562
2.75 0.0920 3.35 0.1435 3.95 0.2128 4.55 0.3030 5.15 0.4173 5.75 0.5588
2.76 0.0927 3.36 0.1445 3.96 0.2141 4.56 0.3047 5.16 0.4194 5.76 0.5615
2.77 0.0934 3.37 0.1455 3.97 0.2154 4.57 0.3064 5.17 0.4216 5.77 0.5641
2.78 0.0942 3.38 0.1465 3.98 0.2168 4.58 0.3081 5.18 0.4237 5.78 0.5667
2.79 0.0949 3.39 0.1475 3.99 0.2181 4.59 0.3098 5.19 0.4258 5.79 0.5693
2.80 0.0957 3.40 0.1485 4.00 0.2194 4.60 0.3116 5.20 0.4280 5.80 0.5720
2.81 0.0964 3.41 0.1496 4.01 0.2208 4.61 0.3133 5.21 0.4302 5.81 0.5746
2.82 0.0972 3.42 0.1506 4.02 0.2222 4.62 0.3150 5.22 0.4323 5.82 0.5773
2.83 0.0979 3.43 0.1516 4.03 0.2235 4.63 0.3168 5.23 0.4345 5.83 0.5799
2.84 0.0987 3.44 0.1527 4.04 0.2249 4.64 0.3185 5.24 0.4367 5.84 0.5826
2.85 0.0994 3.45 0.1537 4.05 0.2263 4.65 0.3203 5.25 0.4389 5.85 0.5853
2.86 0.1002 3.46 0.1548 4.06 0.2277 4.66 0.3220 5.26 0.4411 5.86 0.5880
2.87 0.1010 3.47 0.1558 4.07 0.2290 4.67 0.3238 5.27 0.4433 5.87 0.5907
2.88 0.1018 3.48 0.1569 4.08 0.2304 4.68 0.3256 5.28 0.4455 5.88 0.5934
2.89 0.1026 3.49 0.1579 4.09 0.2318 4.69 0.3274 5.29 0.4478 5.89 0.5961
2.90 0.1033 3.50 0.1590 4.10 0.2332 4.70 0.3292 5.30 0.4500 5.90 0.5989
2.91 0.1041 3.51 0.1601 4.11 0.2347 4.71 0.3310 5.31 0.4522 5.91 0.6016
2.92 0.1049 3.52 0.1612 4.12 0.2361 4.72 0.3328 5.32 0.4545 5.92 0.6043
2.93 0.1057 3.53 0.1623 4.13 0.2375 4.73 0.3346 5.33 0.4568 5.93 0.6071
2.94 0.1065 3.54 0.1633 4.14 0.2389 4.74 0.3364 5.34 0.4590 5.94 0.6099
2.95 0.1074 3.55 0.1644 4.15 0.2404 4.75 0.3383 5.35 0.4613 5.95 0.6126
2.96 0.1082 3.56 0.1655 4.16 0.2418 4.76 0.3401
...
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