ASTM C885-87(2002)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.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:C 885–87 (Reapproved 2002)
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.
1. Scope use of a vibrating driver that transforms an initial electrical
signal into a mechanical vibration. A detector senses the
1.1 This test method covers a procedure for measuring the
resultingmechanicalvibrationsofthespecimenandtransforms
resonance frequency in the flexural (transverse) mode of
them into an electrical signal that can be displayed on the
vibration of rectangular refractory brick or rectangularly
screen of an oscilloscope to detect resonance by a Lissajous
shaped monoliths at room temperature. Young’s modulus is
figure.The calculation ofYoung’s modulus from the resonance
calculated from the resonance frequency of the shape, its mass
frequency measured is simplified by assuming that Poisson’s
(weight) and dimensions.
ratio is ⁄6 for all refractory materials.
1.2 This standard does not purport to address all of the
safety concerns, if any,associated with its use. It is the
4. Significance and Use
responsibility of the user of this standard to establish appro-
4.1 Young’s modulus is a fundamental mechanical property
priate safety and health practices and determine the applica-
of a material.
bility of regulatory limitations prior to use.
4.2 This test method is used to determine the dynamic
2. Referenced Documents modulus of elasticity of rectangular shapes. Since the test is
nondestructive, specimens may be used for other tests as
2.1 ASTM Standards:
desired.
C 134 Test Methods for Size, Dimensional Measurements,
4.3 Thistestmethodisusefulforresearchand development,
and Bulk Density of Refractory Brick and Insulating
engineering application and design, manufacturing process
Firebrick
control, and for developing purchasing specifications.
C 215 Test Method for Fundamental Transverse, Longitu-
4.4 The fundamental assumption inherent in this test
dinal, and Torsional Frequencies of Concrete Specimens
method is that a Poisson’s ratio of ⁄6 is typical for heteroge-
C 623 Test Method for Young’s Modulus, Shear Modulus,
neous refractory materials. The actual Poisson’s ratio may
and Poisson’s Ratio for Glass and Glass-Ceramics by
differ.
Resonance
C 747 Test Method for Moduli of Elasticity and Fundamen-
5. Apparatus
tal Frequencies of Carbon and Graphite Materials by Sonic
2 5.1 A block diagram of a suggested test apparatus arrange-
Resonance
ment is shown in Fig. 1. Details of the equipment are as
C 848 Test Method for Young’s Modulus, Shear Modulus,
follows:
and Poisson’s Ratio for Ceramic Whitewares by Reso-
4 5.1.1 Audio Oscillator, having a continuously variable
nance
calibrated-frequency output from about 50 Hz to at least 10
3. Summary of Test Method kHz.
5.1.2 Audio Amplifier, having a power output sufficient to
3.1 Test specimens are vibrated in flexure over a broad
ensure that the type of driver used can excite the specimen; the
frequency range; mechanical excitation is provided through the
output of the amplifier must be adjustable.
5.1.3 Driver, which may consist of a transducer or a
This test method is under the jurisdiction of ASTM Committee C-8 on
loudspeaker from which the cone has been removed and
Refractories, and is the direct responsibility of Subcommittee C08.01 on Strength
replaced with a probe (connecting rod) oriented parallel to the
Properties.
direction of the vibration; suitable vibration-isolating mounts.
Current edition approved July 31, 1987. Published August 1987. Originally
{1
published as C 885 – 78. Last previous edition C 885 – 81 .
NOTE 1—For small specimens, an air column may preferably be used
Annual Book of ASTM Standards, Vol 15.01.
for “coupling” the loudspeaker to the specimen.
Annual Book of ASTM Standards, Vol 04.02.
Annual Book of ASTM Standards, Vol 15.02.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
C 885–87 (2002)
FIG. 1 Block Diagram of Apparatus
5.1.4 Detector, which may be a transducer or a balance-
mounted monaural (crystal or magnetic) phonograph pick-up
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.
FIG. 2 Typical Specimen Positioning for Measurement of Flexural
5.1.6 Indicating Devices, including an oscilloscope, a reso-
Resonance
nance indicator (voltmeter or ammeter), and a frequency
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.
material. Measure the mass (weight) and dimensions of the dry
5.1.7 Specimen Support, consisting of two knife edges (can
specimens in accordance with Test Methods C 134 and record.
be steel, rubber-coated steel, or medium-hard rubber) of a
length at least equal to the width of the specimens; the distance
7. Procedure
between the knife edges must be adjustable.
7.1 Refractories can vary markedly in their response to the
NOTE 2—The support for the knife edges may be a foam rubber pad,
driver’s frequency; the geometry of the specimens also plays a
and should be vibration-isolated from drive and detector supports.
significant role in their response characteristics. Variations in
NOTE 3—Alternatively, knife edges can be omitted and the specimen
the following procedure are permissible as long as flexural and
may be placed directly on a foam rubber pad if the test material is easily
fundamental resonance are verified (Note 6 and Note 7). Fig. 2
excitable due to its composition and geometry.
and Fig. 3 illustrate a typical specimen positioning and the
6. Sampling and Specimen Preparation
desired mode of vibration, respectively.
7.2 Sample Placement—Place the specimen “flat” (thick-
6.1 Specimensmustberectangularprisms.Theymaybefull
ness dimension perpendicular to supports) on parallel knife
straight brick or rectangular samples cut from brick shapes;
edges at 0.224 l (where l is the length of the specimen) from its
rectangular straight shapes of monolithic refractories, or rect-
ends. Optionally, the specimen can be placed on a foam rubber
angularspecimenscutfrommonolithicshapes.Forbestresults,
pad.
their length to thickness ratio should be at least 3 to 1.
7.3 Driver Placement—Place the driver preferably at the
Maximumspecimensizeandmassareprimarilydeterminedby
center of the top or bottom face of the specimen using
the test system’s energy capability and by the resonance
moderate balanced pressure or spring action.
response characteristics of the material. Minimum specimen
size and mass are primarily determined by adequate and
NOTE 4—Especially with small (thin) specimens, the lightest possible
optimum coupling of the driver and the detector to the
driver pressure to ensure adequate “coupling” must be used in order to
specimen, and by the resonance response characteristics of the achieve proper resonance response. In small specimens, exact placement
C 885–87 (2002)
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
0.224 l) shall cause a Lissajous pattern and high output at the resonance
indicator to disappear.
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
FIG. 3 Fundamental Mode of Vibration in Flexure (Side View)
detector is placed at the end center or at the top center of the specimen.
8. Calculation
of the driver at the very center of the flat specimen is important; also, an
8.1 Data determined on individual specimens include:
air column may be used for “coupling.”
8.1.1 l = length of specimen, in.,
7.4 Detector Placement—Place the detector preferably at
8.1.2 b = width of specimen, in.,
one end of the specimen and at the center of either the width or
8.1.3 t = thickness of specimen, in.,
thickness (considering the orientation of maximum response of
8.1.4 w = mass (weight) of specimen, lb, and
the detector) using minimal pressure.
8.1.5 f = fundamental flexural resonance frequency, Hz.
8.2 CalculateYoung’s modulus E, in psi, of the specimen as
NOTE 5—Make sure that the stylus of the phonograph cartridge (if
used) is well secured.
follows:
7.5 Activate and warm up the equipment so that power
E 5 C · w · f (1)
adequate to excite the specimen is delivered to the driver. Set
2 2
where C =[C b]/b (in s /in. ) is calculated from values of
1 1
the gain on the detector circuit high enough to detect vibration
[C b] listed in Table 1 for various l/t ratios based on Pickett’s
in the specimen, and to display it on the oscilloscope screen
equations solved for a Poisson’s ratio of ⁄6 . Alternatively,
with sufficient amplitude to measure accurately the frequency
[C b] can be computed directly from l and t using Pickett’s
at which the signal amplitude is maximized. Adjust the
original equations and correction factors, as described in
oscilloscope so that a sharply defined horizontal baseline exists
Appendix X1.
when the specimen is not excited. Scan frequency with the
audio oscillator until fundamental flexural specimen resonance
is indicated by an oval to circular Lissajous figure at the
Pickett, G., “Equations for Computing Elastic Constants from Flexural and
oscilloscope and maximum output is shown at the resonance
Torsional Resonant Frequencies of Vibration of Prisms and Cylinders,” Proceed-
indicator. Record the resonance frequency. ings, 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
C 885–87 (2002)
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
2.80 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 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 6.00 0.6266
3.01 0.1123 3.61 0.1711 4.21 0.2491 4.81 0.3494 5.41 0.4751 6.01 0.6294
3.02 0.1131 3.62 0.1723 4.22 0.2506 4.82 0.3513 5.42 0.4774 6.02 0.6323
3.03 0.1140 3.63 0.1734 4.23 0.2521 4.83 0.3531 5.43 0.4798 6.03 0.6351
3.04 0.1148 3.64 0.1746 4.24 0.2536 4.84 0.3550 5.44 0.4821 6.04 0.6380
3.05 0.1157 3.65 0.1757 4.25 0.2551 4.85 0.3569 5.45 0.4845 6.05 0.6408
3.06 0.1166 3.66 0.1769 4.26 0.2566 4.86 0.3588 5.46 0.4868 6.06 0.6437
3.07 0.1174 3.67 0.1780 4.27 0.2581 4.87 0.3608 5.47 0.4892 6.07 0.6466
3.08 0.1183 3.68 0.1792 4.28 0.2596 4.88 0.3627 5.48 0.4916 6.08 0.6495
3.09 0.1192 3.69 0.1804 4.29 0.2611 4.89 0.3646 5.49
...