ASTM C885-87(1997)e1

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.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.
e1
Designation: C 885 – 87 (Reapproved 1997)
AMERICAN SOCIETY FOR TESTING AND MATERIALS
100 Barr Harbor Dr., West Conshohocken, PA 19428
Reprinted from the Annual Book of ASTM Standards. Copyright ASTM
Standard Test Method for
Young’s Modulus of Refractory Shapes by Sonic
Resonance
This standard is issued under the fixed designation C 885; 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.
e NOTE—Editorial changes were made in Sections 10 and 11 in November 1997.
1. Scope signal into a mechanical vibration. A detector senses the
resulting mechanical vibrations of the specimen and transforms
1.1 This test method covers a procedure for measuring the
them into an electrical signal that can be displayed on the
resonance frequency in the flexural (transverse) mode of
screen of an oscilloscope to detect resonance by a Lissajous
vibration of rectangular refractory brick or rectangularly
figure. The calculation of Young’s modulus from the resonance
shaped monoliths at room temperature. Young’s modulus is
frequency measured is simplified by assuming that Poisson’s
calculated from the resonance frequency of the shape, its mass
ratio is ⁄6 for all refractory materials.
(weight) and dimensions.
1.2 This standard does not purport to address all of the
4. Significance and Use
safety concerns, if any,associated with its use. It is the
4.1 Young’s modulus is a fundamental mechanical property
responsibility of the user of this standard to establish appro-
of a material.
priate safety and health practices and determine the applica-
4.2 This test method is used to determine the dynamic
bility of regulatory limitations prior to use.
modulus of elasticity of rectangular shapes. Since the test is
2. Referenced Documents nondestructive, specimens may be used for other tests as
desired.
2.1 ASTM Standards:
4.3 This test method is useful for research and development,
C 134 Test Methods for Size, Dimensional Measurements,
engineering application and design, manufacturing process
and Bulk Density of Refractory Brick and Insulating
control, and for developing purchasing specifications.
Firebrick
4.4 The fundamental assumption inherent in this test
C 215 Test Method for Fundamental Transverse, Longitu-
method is that a Poisson’s ratio of ⁄6 is typical for heteroge-
dinal, and Torsional Frequencies of Concrete Specimens
neous refractory materials. The actual Poisson’s ratio may
C 623 Test Method for Young’s Modulus, Shear Modulus,
differ.
and Poisson’s Ratio for Glass and Glass-Ceramics by
Resonance
5. Apparatus
C 747 Test Method for Moduli of Elasticity and Fundamen-
5.1 A block diagram of a suggested test apparatus arrange-
tal Frequencies of Carbon and Graphite Materials by Sonic
2 ment is shown in Fig. 1. Details of the equipment are as
Resonance
follows:
C 848 Test Method for Young’s Modulus, Shear Modulus,
5.1.1 Audio Oscillator, having a continuously variable
and Poisson’s Ratio for Ceramic Whitewares by Reso-
4 calibrated-frequency output from about 50 Hz to at least 10
nance
kHz.
3. Summary of Test Method 5.1.2 Audio Amplifier, having a power output sufficient to
ensure that the type of driver used can excite the specimen; the
3.1 Test specimens are vibrated in flexure over a broad
output of the amplifier must be adjustable.
frequency range; mechanical excitation is provided through the
5.1.3 Driver, which may consist of a transducer or a
use of a vibrating driver that transforms an initial electrical
loudspeaker from which the cone has been removed and
replaced with a probe (connecting rod) oriented parallel to the
This test method is under the jurisdiction of ASTM Committee C-8 on
direction of the vibration; suitable vibration-isolating mounts.
Refractories, and is the direct responsibility of Subcommittee C08.01 on Strength
Properties.
NOTE 1—For small specimens, an air column may preferably be used
Current edition approved July 31, 1987. Published August 1987. Originally
for “coupling” the loudspeaker to the specimen.
{1
published as C 885 – 78. Last previous edition C 885 – 81 .
5.1.4 Detector, which may be a transducer or a balance-
Annual Book of ASTM Standards, Vol 15.01.
Annual Book of ASTM Standards, Vol 04.02.
mounted monaural (crystal or magnetic) phonograph pick-up
Annual Book of ASTM Standards, Vol 15.02.
NOTICE:¬This¬standard¬has¬either¬been¬superceded¬and¬replaced¬by¬a¬new¬version¬or¬discontinued.¬
Contact¬ASTM¬International¬(www.astm.org)¬for¬the¬latest¬information.¬
C 885
FIG. 1 Block Diagram of Apparatus
cartridge of good frequency response; the detector should be
movable across the specimen; suitable vibration-isolating
mounts.
5.1.5 Pre-Scope Amplifier in the detector circuit,
impedance-matched with the detector used; the output must be
adjustable.
5.1.6 Indicating Devices, including an oscilloscope, a reso-
nance indicator (voltmeter or ammeter), and a frequency FIG. 2 Typical Specimen Positioning for Measurement of Flexural
Resonance
indicator, which may be the control dial of the audio-oscillator
(accurately readable to 630 Hz or better) or, preferably, a
7. Procedure
frequency meter, for example, a digital frequency counter.
7.1 Refractories can vary markedly in their response to the
5.1.7 Specimen Support, consisting of two knife edges (can
driver’s frequency; the geometry of the specimens also plays a
be steel, rubber-coated steel, or medium-hard rubber) of a
significant role in their response characteristics. Variations in
length at least equal to the width of the specimens; the distance
the following procedure are permissible as long as flexural and
between the knife edges must be adjustable.
fundamental resonance are verified (Note 6 and Note 7). Fig. 2
NOTE 2—The support for the knife edges may be a foam rubber pad,
and Fig. 3 illustrate a typical specimen positioning and the
and should be vibration-isolated from drive and detector supports.
desired mode of vibration, respectively.
NOTE 3—Alternatively, knife edges can be omitted and the specimen
7.2 Sample Placement—Place the specimen “flat” (thick-
may be placed directly on a foam rubber pad if the test material is easily
ness dimension perpendicular to supports) on parallel knife
excitable due to its composition and geometry.
edges at 0.224 l (where l is the length of the specimen) from its
6. Sampling and Specimen Preparation
ends. Optionally, the specimen can be placed on a foam rubber
pad.
6.1 Specimens must be rectangular prisms. They may be full
7.3 Driver Placement—Place the driver preferably at the
straight brick or rectangular samples cut from brick shapes;
center of the top or bottom face of the specimen using
rectangular straight shapes of monolithic refractories, or rect-
moderate balanced pressure or spring action.
angular specimens cut from monolithic shapes. For best results,
their length to thickness ratio should be at least 3 to 1.
NOTE 4—Especially with small (thin) specimens, the lightest possible
Maximum specimen size and mass are primarily determined by
driver pressure to ensure adequate “coupling” must be used in order to
the test system’s energy capability and by the resonance achieve proper resonance response. In small specimens, exact placement
of the driver at the very center of the flat specimen is important; also, an
response characteristics of the material. Minimum specimen
air column may be used for “coupling.”
size and mass are primarily determined by adequate and
optimum coupling of the driver and the detector to the 7.4 Detector Placement—Place the detector preferably at
specimen, and by the resonance response characteristics of the one end of the specimen and at the center of either the width or
material. Measure the mass (weight) and dimensions of the dry thickness (considering the orientation of maximum response of
specimens in accordance with Test Methods C 134 and record. the detector) using minimal pressure.
NOTICE:¬This¬standard¬has¬either¬been¬superceded¬and¬replaced¬by¬a¬new¬version¬or¬discontinued.¬
Contact¬ASTM¬International¬(www.astm.org)¬for¬the¬latest¬information.¬
C 885
NOTE 7—To verify the fundamental mode of flexural resonance, excite
the specimen at one half of the frequency established in 7.5. A “figure
eight” Lissajous pattern should appear at the oscilloscope when the
detector is placed at the end center or at the top center of the specimen.
8. Calculation
8.1 Data determined on individual specimens include:
FIG. 3 Fundamental Mode of Vibration in Flexure (Side View)
8.1.1 l 5 length of specimen, in.,
8.1.2 b 5 width of specimen, in.,
8.1.3 t 5 thickness of specimen, in.,
NOTE 5—Make sure that the stylus of the phonograph cartridge (if
used) is well secured.
8.1.4 w 5 mass (weight) of specimen, lb, and
8.1.5 f 5 fundamental flexural resonance frequency, Hz.
7.5 Activate and warm up the equipment so that power
8.2 Calculate Young’s modulus E, in psi, of the specimen as
adequate to excite the specimen is delivered to the driver. Set
follows:
the gain on the detector circuit high enough to detect vibration
in the specimen, and to display it on the oscilloscope screen
E 5 C · w · f
with sufficient amplitude to measure accurately the frequency
(1)
at which the signal amplitude is maximized. Adjust the
2 2
oscilloscope so that a sharply defined horizontal baseline exists
where C 5 [C b]/b (in s /in. ) is calculated from values of
1 1
when the specimen is not excited. Scan frequency with the
[C b] listed in Table 1 for various l/t ratios based on Pickett’s
audio oscillator until fundamental flexural specimen resonance 1
equations solved for a Poisson’s ratio of ⁄6. Alternatively,
is indicated by an oval to circular Lissajous figure at the
[C b] can be computed directly from l and t using Pickett’s
oscilloscope and maximum output is shown at the resonance
original equations and correction factors, as described in
indicator. Record the resonance frequency.
Appendix X1.
NOTE 6—To verify the flexural mode of vibration, move the detector to
the top center of the specimen. The oval or circular oscilloscope pattern
shall be maintained. Placement of the detector above the nodal points (at
Pickett, G., “Equations for Computing Elastic Constants from Flexural and
0.224 l) shall cause a Lissajous pattern and high output at the resonance
Torsional Resonant Frequencies of Vibration of Prisms and Cylinders,”
indicator to disappear. 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
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
NOTICE:¬This¬standard¬has¬either¬been¬superceded¬and¬replaced¬by¬a¬new¬version¬or¬discontinued.¬
Contact¬ASTM¬International¬(www.astm.org)¬for¬the¬latest¬information.¬
C 885
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
2.82 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 5.36 0.4636 5.96 0.6154
2.97 0.1090 3.57 0.1667 4.17 0.2433 4.77 0.3419 5.37 0.4659 5.97 0.6182
2.98 0.1098 3.58 0.1678 4.18 0.2447 4.78 0.3438 5.38 0.4682 5.98 0.6210
2.99 0.1106 3.59 0.1689 4.19 0.2462 4.79 0.3456 5.39 0.4705 5.99 0.6238
3.00 0.1115 3.60 0.1700 4.20 0.2476 4.80 0.3475 5.40 0.4728 6.
...