1、Designation: C 885 87 (Reapproved 2007)Standard Test Method forYoungs Modulus of Refractory Shapes by SonicResonance1This standard is issued under the fixed designation C 885; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the yea
2、r of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method covers a procedure for measuring theresonance frequency in the flexural (transverse) mode ofvib
3、ration of rectangular refractory brick or rectangularlyshaped monoliths at room temperature. Youngs modulus iscalculated from the resonance frequency of the shape, its mass(weight) and dimensions.1.2 This standard does not purport to address all of thesafety concerns, if any,associated with its use.
4、 It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2C 134 Test Methods for Size, Dimensional Measurements,and Bulk Density of Ref
5、ractory Brick and InsulatingFirebrickC 215 Test Method for Fundamental Transverse, Longitu-dinal, and Torsional Resonant Frequencies of ConcreteSpecimensC 623 Test Method for Youngs Modulus, Shear Modulus,and Poissons Ratio for Glass and Glass-Ceramics byResonanceC 747 Test Method for Moduli of Elas
6、ticity and Fundamen-tal Frequencies of Carbon and Graphite Materials by SonicResonanceC 848 Test Method for Youngs Modulus, Shear Modulus,and Poissons Ratio For Ceramic Whitewares by Reso-nance3. Summary of Test Method3.1 Test specimens are vibrated in flexure over a broadfrequency range; mechanical
7、 excitation is provided through theuse of a vibrating driver that transforms an initial electricalsignal into a mechanical vibration. A detector senses theresulting mechanical vibrations of the specimen and transformsthem into an electrical signal that can be displayed on thescreen of an oscilloscop
8、e to detect resonance by a Lissajousfigure. The calculation of Youngs modulus from the resonancefrequency measured is simplified by assuming that Poissonsratio is16 for all refractory materials.4. Significance and Use4.1 Youngs modulus is a fundamental mechanical propertyof a material.4.2 This test
9、method is used to determine the dynamicmodulus of elasticity of rectangular shapes. Since the test isnondestructive, specimens may be used for other tests asdesired.4.3 This test method is useful for research and development,engineering application and design, manufacturing processcontrol, and for d
10、eveloping purchasing specifications.4.4 The fundamental assumption inherent in this testmethod is that a Poissons ratio of16 is typical for heteroge-neous refractory materials. The actual Poissons ratio maydiffer.5. Apparatus5.1 A block diagram of a suggested test apparatus arrange-ment is shown in
11、Fig. 1. Details of the equipment are asfollows:5.1.1 Audio Oscillator, having a continuously variablecalibrated-frequency output from about 50 Hz to at least 10kHz.5.1.2 Audio Amplifier, having a power output sufficient toensure that the type of driver used can excite the specimen; theoutput of the
12、amplifier must be adjustable.5.1.3 Driver, which may consist of a transducer or aloudspeaker from which the cone has been removed andreplaced with a probe (connecting rod) oriented parallel to thedirection of the vibration; suitable vibration-isolating mounts.NOTE 1For small specimens, an air column
13、 may preferably be usedfor “coupling” the loudspeaker to the specimen.1This test method is under the jurisdiction of ASTM Committee C08 onRefractories and is the direct responsibility of Subcommittee C08.01 on Strength.Current edition approved March 1, 2007. Published April 2007. Originallyapproved
14、in 1978. Last previous edition approved in 2002 as C 885 87 (2002).2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM we
15、bsite.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.5.1.4 Detector, which may be a transducer or a balance-mounted monaural (crystal or magnetic) phonograph pick-upcartridge of good frequency response; the detector should bemovable
16、 across the specimen; suitable vibration-isolatingmounts.5.1.5 Pre-Scope Amplifier in the detector circuit,impedance-matched with the detector used; the output must beadjustable.5.1.6 Indicating Devices, including an oscilloscope, a reso-nance indicator (voltmeter or ammeter), and a frequencyindicat
17、or, which may be the control dial of the audio-oscillator(accurately readable to 630 Hz or better) or, preferably, afrequency meter, for example, a digital frequency counter.5.1.7 Specimen Support, consisting of two knife edges (canbe steel, rubber-coated steel, or medium-hard rubber) of alength at
18、least equal to the width of the specimens; the distancebetween the knife edges must be adjustable.NOTE 2The support for the knife edges may be a foam rubber pad,and should be vibration-isolated from drive and detector supports.NOTE 3Alternatively, knife edges can be omitted and the specimenmay be pl
19、aced directly on a foam rubber pad if the test material is easilyexcitable due to its composition and geometry.6. Sampling and Specimen Preparation6.1 Specimens must be rectangular prisms. They may be fullstraight brick or rectangular samples cut from brick shapes;rectangular straight shapes of mono
20、lithic refractories, or rect-angular specimens cut from monolithic shapes. For best results,their length to thickness ratio should be at least 3 to 1.Maximum specimen size and mass are primarily determined bythe test systems energy capability and by the resonanceresponse characteristics of the mater
21、ial. Minimum specimensize and mass are primarily determined by adequate andoptimum coupling of the driver and the detector to thespecimen, and by the resonance response characteristics of thematerial. Measure the mass (weight) and dimensions of the dryspecimens in accordance with Test Methods C 134
22、and record.7. Procedure7.1 Refractories can vary markedly in their response to thedrivers frequency; the geometry of the specimens also plays asignificant role in their response characteristics. Variations inthe following procedure are permissible as long as flexural andfundamental resonance are ver
23、ified (Note 6 and Note 7). Fig. 2and Fig. 3 illustrate a typical specimen positioning and thedesired mode of vibration, respectively.7.2 Sample PlacementPlace the specimen “flat” (thick-ness dimension perpendicular to supports) on parallel knifeedges at 0.224 l (where l is the length of the specimen
24、) from itsends. Optionally, the specimen can be placed on a foam rubberpad.7.3 Driver PlacementPlace the driver preferably at thecenter of the top or bottom face of the specimen usingmoderate balanced pressure or spring action.NOTE 4Especially with small (thin) specimens, the lightest possibledriver
25、 pressure to ensure adequate “coupling” must be used in order toachieve proper resonance response. In small specimens, exact placementFIG. 1 Block Diagram of ApparatusFIG. 2 Typical Specimen Positioning for Measurement of FlexuralResonanceC 885 87 (2007)2of the driver at the very center of the flat
26、specimen is important; also, anair column may be used for “coupling.”7.4 Detector PlacementPlace the detector preferably atone end of the specimen and at the center of either the width orthickness (considering the orientation of maximum response ofthe detector) using minimal pressure.NOTE 5Make sure
27、 that the stylus of the phonograph cartridge (ifused) is well secured.7.5 Activate and warm up the equipment so that poweradequate to excite the specimen is delivered to the driver. Setthe gain on the detector circuit high enough to detect vibrationin the specimen, and to display it on the oscillosc
28、ope screenwith sufficient amplitude to measure accurately the frequencyat which the signal amplitude is maximized. Adjust theoscilloscope so that a sharply defined horizontal baseline existswhen the specimen is not excited. Scan frequency with theaudio oscillator until fundamental flexural specimen
29、resonanceis indicated by an oval to circular Lissajous figure at theoscilloscope and maximum output is shown at the resonanceindicator. Record the resonance frequency.NOTE 6To verify the flexural mode of vibration, move the detector tothe top center of the specimen. The oval or circular oscilloscope
30、 patternshall be maintained. Placement of the detector above the nodal points (at0.224 l) shall cause a Lissajous pattern and high output at the resonanceindicator to disappear.NOTE 7To verify the fundamental mode of flexural resonance, excitethe specimen at one half of the frequency established in
31、7.5. A “figureeight” Lissajous pattern should appear at the oscilloscope when thedetector is placed at the end center or at the top center of the specimen.8. Calculation8.1 Data determined on individual specimens include:8.1.1 l = length of specimen, in.,8.1.2 b = width of specimen, in.,8.1.3 t = th
32、ickness of specimen, in.,8.1.4 w = mass (weight) of specimen, lb, and8.1.5 f = fundamental flexural resonance frequency, Hz.8.2 Calculate Youngs modulus E, in psi, of the specimen asfollows:E 5 C1 w f2(1)where C1=C1b/b (in s2/in.2) is calculated from values ofC1b listed in Table 1 for various l/t ra
33、tios based on Picketts3equations solved for a Poissons ratio of16 . Alternatively,C1b can be computed directly from l and t using Pickettsoriginal equations and correction factors, as described inAppendix X1.TABLE 1 C1b Valuesl/t C1b l/t C1b l/t C1b l/t C1b l/t C1b l/t C1b2.50 0.0750 3.10 0.1200 3.7
34、0 0.1815 4.30 0.2627 4.90 0.3665 5.50 0.49632.51 0.0756 3.11 0.1209 3.71 0.1827 4.31 0.2642 4.91 0.3685 5.51 0.49882.52 0.0763 3.12 0.1218 3.72 0.1839 4.32 0.2657 4.92 0.3704 5.52 0.50122.53 0.0769 3.13 0.1227 3.73 0.1851 4.33 0.2673 4.93 0.3724 5.53 0.50362.54 0.0776 3.14 0.1236 3.74 0.1863 4.34 0.
35、2688 4.94 0.3743 5.54 0.50602.55 0.0782 3.15 0.1245 3.75 0.1875 4.35 0.2704 4.95 0.3763 5.55 0.50842.56 0.0789 3.16 0.1254 3.76 0.1887 4.36 0.2720 4.96 0.3783 5.56 0.51092.57 0.0795 3.17 0.1263 3.77 0.1899 4.37 0.2735 4.97 0.3803 5.57 0.51332.58 0.0802 3.18 0.1272 3.78 0.1911 4.38 0.2751 4.98 0.3823
36、 5.58 0.51582.59 0.0808 3.19 0.1281 3.79 0.1924 4.39 0.2767 4.99 0.3843 5.59 0.51832.60 0.0815 3.20 0.1291 3.80 0.1936 4.40 0.2783 5.00 0.3863 5.60 0.52072.61 0.0822 3.21 0.1300 3.81 0.1948 4.41 0.2799 5.01 0.3883 5.61 0.52322.62 0.0828 3.22 0.1309 3.82 0.1961 4.42 0.2815 5.02 0.3903 5.62 0.52572.63
37、 0.0835 3.23 0.1318 3.83 0.1973 4.43 0.2831 5.03 0.3924 5.63 0.52822.64 0.0842 3.24 0.1328 3.84 0.1986 4.44 0.2847 5.04 0.3944 5.64 0.53072.65 0.0849 3.25 0.1337 3.85 0.1999 4.45 0.2864 5.05 0.3964 5.65 0.53322.66 0.0856 3.26 0.1347 3.86 0.2011 4.46 0.2880 5.06 0.3985 5.66 0.53582.67 0.0863 3.27 0.1
38、356 3.87 0.2024 4.47 0.2896 5.07 0.4005 5.67 0.53832.68 0.0870 3.28 0.1366 3.88 0.2037 4.48 0.2913 5.08 0.4026 5.68 0.54082.69 0.0877 3.29 0.1376 3.89 0.2050 4.49 0.2929 5.09 0.4047 5.69 0.54342.70 0.0884 3.30 0.1385 3.90 0.2062 4.50 0.2946 5.10 0.4068 5.70 0.54592.71 0.0891 3.31 0.1395 3.91 0.2075
39、4.51 0.2963 5.11 0.4089 5.71 0.54852.72 0.0898 3.32 0.1405 3.92 0.2088 4.52 0.2979 5.12 0.4110 5.72 0.55112.73 0.0905 3.33 0.1415 3.93 0.2101 4.53 0.2996 5.13 0.4131 5.73 0.55372.74 0.0912 3.34 0.1425 3.94 0.2115 4.54 0.3013 5.14 0.4152 5.74 0.55622.75 0.0920 3.35 0.1435 3.95 0.2128 4.55 0.3030 5.15
40、 0.4173 5.75 0.55882.76 0.0927 3.36 0.1445 3.96 0.2141 4.56 0.3047 5.16 0.4194 5.76 0.56152.77 0.0934 3.37 0.1455 3.97 0.2154 4.57 0.3064 5.17 0.4216 5.77 0.56412.78 0.0942 3.38 0.1465 3.98 0.2168 4.58 0.3081 5.18 0.4237 5.78 0.56672.79 0.0949 3.39 0.1475 3.99 0.2181 4.59 0.3098 5.19 0.4258 5.79 0.5
41、6933Pickett, G., “Equations for Computing Elastic Constants from Flexural andTorsional Resonant Frequencies of Vibration of Prisms and Cylinders,” Proceed-ings, ASTM, Vol 45, 1945, pp. 846863.FIG. 3 Fundamental Mode of Vibration in Flexure (Side View)C 885 87 (2007)3TABLE 1 Continuedl/t C1b l/t C1b
42、l/t C1b l/t C1b l/t C1b l/t C1b2.80 0.0957 3.40 0.1485 4.00 0.2194 4.60 0.3116 5.20 0.4280 5.80 0.57202.81 0.0964 3.41 0.1496 4.01 0.2208 4.61 0.3133 5.21 0.4302 5.81 0.57462.82 0.0972 3.42 0.1506 4.02 0.2222 4.62 0.3150 5.22 0.4323 5.82 0.57732.83 0.0979 3.43 0.1516 4.03 0.2235 4.63 0.3168 5.23 0.4
43、345 5.83 0.57992.84 0.0987 3.44 0.1527 4.04 0.2249 4.64 0.3185 5.24 0.4367 5.84 0.58262.85 0.0994 3.45 0.1537 4.05 0.2263 4.65 0.3203 5.25 0.4389 5.85 0.58532.86 0.1002 3.46 0.1548 4.06 0.2277 4.66 0.3220 5.26 0.4411 5.86 0.58802.87 0.1010 3.47 0.1558 4.07 0.2290 4.67 0.3238 5.27 0.4433 5.87 0.59072
44、.88 0.1018 3.48 0.1569 4.08 0.2304 4.68 0.3256 5.28 0.4455 5.88 0.59342.89 0.1026 3.49 0.1579 4.09 0.2318 4.69 0.3274 5.29 0.4478 5.89 0.59612.90 0.1033 3.50 0.1590 4.10 0.2332 4.70 0.3292 5.30 0.4500 5.90 0.59892.91 0.1041 3.51 0.1601 4.11 0.2347 4.71 0.3310 5.31 0.4522 5.91 0.60162.92 0.1049 3.52
45、0.1612 4.12 0.2361 4.72 0.3328 5.32 0.4545 5.92 0.60432.93 0.1057 3.53 0.1623 4.13 0.2375 4.73 0.3346 5.33 0.4568 5.93 0.60712.94 0.1065 3.54 0.1633 4.14 0.2389 4.74 0.3364 5.34 0.4590 5.94 0.60992.95 0.1074 3.55 0.1644 4.15 0.2404 4.75 0.3383 5.35 0.4613 5.95 0.61262.96 0.1082 3.56 0.1655 4.16 0.24
46、18 4.76 0.3401 5.36 0.4636 5.96 0.61542.97 0.1090 3.57 0.1667 4.17 0.2433 4.77 0.3419 5.37 0.4659 5.97 0.61822.98 0.1098 3.58 0.1678 4.18 0.2447 4.78 0.3438 5.38 0.4682 5.98 0.62102.99 0.1106 3.59 0.1689 4.19 0.2462 4.79 0.3456 5.39 0.4705 5.99 0.62383.00 0.1115 3.60 0.1700 4.20 0.2476 4.80 0.3475 5
47、.40 0.4728 6.00 0.62663.01 0.1123 3.61 0.1711 4.21 0.2491 4.81 0.3494 5.41 0.4751 6.01 0.62943.02 0.1131 3.62 0.1723 4.22 0.2506 4.82 0.3513 5.42 0.4774 6.02 0.63233.03 0.1140 3.63 0.1734 4.23 0.2521 4.83 0.3531 5.43 0.4798 6.03 0.63513.04 0.1148 3.64 0.1746 4.24 0.2536 4.84 0.3550 5.44 0.4821 6.04
48、0.63803.05 0.1157 3.65 0.1757 4.25 0.2551 4.85 0.3569 5.45 0.4845 6.05 0.64083.06 0.1166 3.66 0.1769 4.26 0.2566 4.86 0.3588 5.46 0.4868 6.06 0.64373.07 0.1174 3.67 0.1780 4.27 0.2581 4.87 0.3608 5.47 0.4892 6.07 0.64663.08 0.1183 3.68 0.1792 4.28 0.2596 4.88 0.3627 5.48 0.4916 6.08 0.64953.09 0.119
49、2 3.69 0.1804 4.29 0.2611 4.89 0.3646 5.49 0.4940 6.09 0.65246.10 0.6553 6.40 0.7466 6.70 0.8465 7.00 0.9552 8.30 1.5383 9.75 2.43366.11 0.6582 6.41 0.7498 6.71 0.8499 7.05 0.9742 8.35 1.5647 9.80 2.46966.12 0.6611 6.42 0.7530 6.72 0.8534 7.10 0.9934 8.40 1.5913 9.85 2.50596.13 0.6640 6.43 0.7562 6.73 0.8569 7.15 1.0130 8.45 1.6183 9.90 2.54276.14 0.6670 6.44 0.7594 6.74 0.8604 7.20 1.0327 8.50 1.6455 9.95 2.57976.15 0.6699 6.45 0.7627 6.75 0.8640 7.25 1.0528 8.55 1.6731 10.00 2.61726.16 0.6729 6.46 0.7659 6.76 0.867
