1、Designation: C885 87 (Reapproved 2012)Standard Test Method forYoungs Modulus of Refractory Shapes by SonicResonance1This standard is issued under the fixed designation C885; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year
2、of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () 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 ofvibrat
3、ion 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 UnitsThe values stated in inch-pound units are to beregarded as standard. The values given in parenthes
4、es aremathematical conversions to SI units that are provided forinformation only and are not considered standard.1.2.1 Although the Hertz (Hz) is an SI unit, it is derivedfrom seconds which is also an inch-pound unit.1.3 This standard does not purport to address all of thesafety concerns, if any,ass
5、ociated with its use. 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:2C134 Test Methods for Size, Dimensional Measurements,and
6、 Bulk Density of Refractory Brick and InsulatingFirebrickC215 Test Method for Fundamental Transverse, Longitudi-nal, and Torsional Resonant Frequencies of ConcreteSpecimensC623 Test Method for Youngs Modulus, Shear Modulus,and Poissons Ratio for Glass and Glass-Ceramics byResonanceC747 Test Method f
7、or Moduli of Elasticity and Fundamen-tal Frequencies of Carbon and Graphite Materials by SonicResonanceC848 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 r
8、ange; mechanical 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 o
9、f an oscilloscope 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 materia
10、l.4.2 This test 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 processco
11、ntrol, and for developing 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-m
12、ent is shown in 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.1This test method is under the jurisdiction of ASTM Committee C08 onRefractories and is the direct responsibility of Sub
13、committee C08.01 on Strength.Current edition approved March 1, 2012. Published April 2012. Originallyapproved in 1978. Last previous edition approved in 2007 as C885 87 (2007)1.DOI: 10.1520/C0885-87R12.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Serv
14、ice at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.5.1.2 Audio Amplifier, having a power output
15、 sufficient toensure that the type of driver used can excite the specimen; theoutput of the 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
16、 the vibration; suitable vibration-isolating mounts.NOTE 1For small specimens, an air column may preferably be usedfor “coupling” the loudspeaker to the specimen.5.1.4 Detector, which may be a transducer or a balance-mounted monaural (crystal or magnetic) phonograph pick-upcartridge of good frequenc
17、y response; the detector should bemovable 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 (volt
18、meter or ammeter), and a frequencyindicator, which may be the control dial of the audio-oscillator(accurately readable to 6 30 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 st
19、eel, or medium-hard rubber) of alength at 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 edge
20、s can be omitted and the specimenmay be placed 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
21、shapes;rectangular straight shapes of monolithic 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 reso
22、nanceresponse characteristics of the material. 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 dryspecim
23、ens in accordance with Test Methods C134 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
24、flexural andfundamental resonance are verified (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 knifeFIG. 1 Block D
25、iagram of ApparatusFIG. 2 Typical Specimen Positioning for Measurement of FlexuralResonanceC885 87 (2012)2edges at 0.224 l (where l is the length of the specimen) from itsends. Optionally, the specimen can be placed on a foam rubberpad.7.3 Driver PlacementPlace the driver preferably at thecenter of
26、the top or bottom face of the specimen usingmoderate balanced pressure or spring action.NOTE 4Especially with small (thin) specimens, the lightest possibledriver pressure to ensure adequate “coupling” must be used in order toachieve proper resonance response. In small specimens, exact placementof th
27、e driver at the very center of the flat 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
28、) using minimal pressure.NOTE 5Make sure 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 spec
29、imen, and to display it on the oscilloscope 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 oscilla
30、tor until fundamental flexural specimen 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 spe
31、cimen. The oval or circular oscilloscope 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 o
32、ne half of the frequency established in 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
33、 b = width of specimen, in.,8.1.3 t = thickness 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 of
34、C1b listed in Table 1 for various l/t ratios 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/
35、t C1b l/t C1b2.50 0.0750 3.10 0.1200 3.70 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 0.50362.5
36、4 0.0776 3.14 0.1236 3.74 0.1863 4.34 0.2688 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.
37、1272 3.78 0.1911 4.38 0.2751 4.98 0.3823 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
38、 4.42 0.2815 5.02 0.3903 5.62 0.52572.63 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 5.0
39、6 0.3985 5.66 0.53582.67 0.0863 3.27 0.1356 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.
40、54592.71 0.0891 3.31 0.1395 3.91 0.2075 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 0.55113Pickett, G., “Equations for Computing Elastic Constants from Flexural andTorsional Resonant Frequencies of Vibration of Prisms and Cylinders,” Proceed-in
41、gs, ASTM, Vol 45, 1945, pp. 846863.FIG. 3 Fundamental Mode of Vibration in Flexure (Side View)C885 87 (2012)3TABLE 1 Continuedl/t C1b l/t C1b l/t C1b l/t C1b l/t C1b l/t C1b2.73 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 0.4
42、152 5.74 0.55622.75 0.0920 3.35 0.1435 3.95 0.2128 4.55 0.3030 5.15 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
43、.79 0.0949 3.39 0.1475 3.99 0.2181 4.59 0.3098 5.19 0.4258 5.79 0.56932.80 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
44、0.1516 4.03 0.2235 4.63 0.3168 5.23 0.4345 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 0.22
45、90 4.67 0.3238 5.27 0.4433 5.87 0.59072.88 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
46、.31 0.4522 5.91 0.60162.92 0.1049 3.52 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
47、0.61262.96 0.1082 3.56 0.1655 4.16 0.2418 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 0.111
48、5 3.60 0.1700 4.20 0.2476 4.80 0.3475 5.40 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.
49、24 0.2536 4.84 0.3550 5.44 0.4821 6.04 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 0.1192 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
