1、Designation: C848 88 (Reapproved 2016)Standard Test Method forYoungs Modulus, Shear Modulus, and Poissons Ratio ForCeramic Whitewares by Resonance1This standard is issued under the fixed designation C848; the number immediately following the designation indicates the year oforiginal adoption or, in
2、the case of revision, the year 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 the determination of the elasticproperties of ceramic whitew
3、are materials. Specimens of thesematerials possess specific mechanical resonance frequencieswhich are defined by the elastic moduli, density, and geometryof the test specimen. Therefore the elastic properties of amaterial can be computed if the geometry, density, and me-chanical resonance frequencie
4、s of a suitable test specimen ofthat material can be measured. Youngs modulus is determinedusing the resonance frequency in the flexural mode of vibra-tion. The shear modulus, or modulus of rigidity, is found usingtorsional resonance vibrations. Youngs modulus and shearmodulus are used to compute Po
5、issons ratio, the factor oflateral contraction.1.2 All ceramic whiteware materials that are elastic,homogeneous, and isotropic may be tested by this test method.2This test method is not satisfactory for specimens that havecracks or voids that represent inhomogeneities in the material;neither is it s
6、atisfactory when these materials cannot beprepared in a suitable geometry.NOTE 1Elastic here means that an application of stress within theelastic limit of that material making up the body being stressed will causean instantaneous and uniform deformation, which will cease upon removalof the stress,
7、with the body returning instantly to its original size and shapewithout an energy loss. Many ceramic whiteware materials conform to thisdefinition well enough that this test is meaningful.NOTE 2Isotropic means that the elastic properties are the same in alldirections in the material.1.3 A cryogenic
8、cabinet and high-temperature furnace aredescribed for measuring the elastic moduli as a function oftemperature from 195 to 1200C.1.4 Modification of the test for use in quality control ispossible. A range of acceptable resonance frequencies isdetermined for a piece with a particular geometry and den
9、sity.Any specimen with a frequency response falling outside thisfrequency range is rejected. The actual modulus of each pieceneed not be determined as long as the limits of the selectedfrequency range are known to include the resonance frequencythat the piece must possess if its geometry and density
10、 arewithin specified tolerances.1.5 This standard does not purport to address all of thesafety concerns, if any, associated 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 limitati
11、ons prior to use.2. Summary of Test Method2.1 This test method measures the resonance frequencies oftest bars of suitable geometry by exciting them at continuouslyvariable frequencies. Mechanical excitation of the specimen isprovided through use of a transducer that transforms an initialelectrical s
12、ignal into a mechanical vibration. Another trans-ducer senses the resulting mechanical vibrations of the speci-men and transforms them into an electrical signal that can bedisplayed on the screen of an oscilloscope to detect resonance.The resonance frequencies, the dimensions, and the mass of thespe
13、cimen are used to calculate Youngs modulus and the shearmodulus.3. Significance and Use3.1 This test system has advantages in certain respects overthe use of static loading systems in the measurement of ceramicwhitewares.3.1.1 Only minute stresses are applied to the specimen, thusminimizing the poss
14、ibility of fracture.3.1.2 The period of time during which stress is applied andremoved is of the order of hundreds of microseconds, makingit feasible to perform measurements at temperatures wheredelayed elastic and creep effects proceed on a much-shortenedtime scale.3.2 This test method is suitable
15、for detecting whether amaterial meets specifications, if cognizance is given to oneimportant fact: ceramic whiteware materials are sensitive tothermal history. Therefore, the thermal history of a testspecimen must be known before the moduli can be considered1This test method is under the jurisdictio
16、n ofASTM Committee C21 on CeramicWhitewares and Related Productsand is the direct responsibility of SubcommitteeC21.03 on Methods for Whitewares and Environmental Concerns.Current edition approved July 1, 2016. Published July 2016. Originally approvedin 1976. Last previous edition approved in 2011 a
17、s C848 88 (2011). DOI:10.1520/C0848-88R16.2Spinner, S., and Tefft, W. E., “A Method for Determining MechanicalResonance Frequencies and for Calculating Elastic Moduli from TheseFrequencies,” Proceedings, ASTM, 1961, pp. 12211238.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West
18、Conshohocken, PA 19428-2959. United States1in terms of specified values. Material specifications shouldinclude a specific thermal treatment for all test specimens.4. Apparatus4.1 The test apparatus is shown in Fig. 1. It consists of avariable-frequency audio oscillator, used to generate a sinusoi-da
19、l voltage, and a power amplifier and suitable transducer toconvert the electrical signal to a mechanical driving vibration.A frequency meter monitors the audio oscillator output toprovide an accurate frequency determination. A suitablesuspension-coupling system cradles the test specimen, andanother
20、transducer acts to detect mechanical resonance in thespecimen and to convert it into an electrical signal which ispassed through an amplifier and displayed on the vertical platesof an oscilloscope. If a Lissajous figure is desired, the output ofthe oscillator is also coupled to the horizontal plates
21、 of theoscilloscope. If temperature-dependent data are desired, asuitable furnace or cryogenic chamber is used. Details of theequipment are as follows:4.2 Audio Oscillator, having a continuously variable fre-quency output from about 100 to at least 20 kHz. Frequencydrift shall not exceed 1 Hz/min fo
22、r any given setting.4.3 Audio Amplifier, having a power output sufficient toensure that the type of transducer used can excite any specimenthe mass of which falls within a specified range.4.4 TransducersTwo are required; one used as a drivermay be a speaker of the tweeter type or a magnetic cutting
23、heador other similar device, depending on the type of couplingchosen for use between the transducer and the specimen. Theother transducer, used as a detector, may be a crystal ormagnetic reluctance type of phonograph cartridge.Acapacitivepickup may be used if desired. The frequency response of thetr
24、ansducer shall be as good as possible with at least a 6.5-kHzbandwidth before 3-dB power loss occurs.4.5 Power Amplifier, in the detector circuit shall be imped-ance matched with the type of detector transducer selected andshall serve as a prescope amplifier.4.6 Cathode-Ray Oscilloscope, shall be an
25、y model suitablefor general laboratory work.4.7 Frequency Counter, shall be able to measure frequenciesto within 61 Hz.4.8 If data at elevated temperatures are desired, a furnaceshall be used that is capable of controlled heating and cooling.It shall have a specimen zone 180 mm in length, which will
26、 beuniform in temperature within 65C throughout the range oftemperatures encountered in testing.4.9 For data at cryogenic temperatures, any chamber shallsuffice that is capable of controlled heating, frost-free, anduniform in temperature within 65C over the length of thespecimen at any selected temp
27、erature. A suitable cryogenicchamber3is shown in Fig. 2.4.10 Any method of specimen suspension shall be used thatis adequate for the temperatures encountered in testing and thatshall allow the specimen to vibrate without significant restric-tion. Common cotton thread, silica glass fiber thread,Nichr
28、ome, or platinum wire may be used. If metal wiresuspension is used in the furnace, coupling characteristics willbe improved if, outside the temperature zone, the wire iscoupled to cotton thread and the thread is coupled to the3Smith, R. E., and Hagy, H. E., “A Low Temperature Sonic ResonanceApparatu
29、s for Determining Elastic Properties of Solids,” Internal Report 2195,Corning Glass Works, April 1961.FIG. 1 Block Diagram of ApparatusC848 88 (2016)2transducer. If specimen supports of other than the suspensiontype are used, they shall meet the same general specifications.5. Test Specimens5.1 Prepa
30、re the specimens so that they are either rectangularor circular in cross section. Either geometry can be used tomeasure both Youngs modulus and shear modulus. However,great experimental difficulties in obtaining torsional resonancefrequencies for a cylindrical specimen usually preclude its usein det
31、ermining shear modulus, although the equations forcomputing shear modulus with a cylindrical specimen are bothsimpler and more accurate than those used with a prismatic bar.5.2 Resonance frequencies for a given specimen are func-tions of the bar dimensions as well as its density and modulus;therefor
32、e, dimensions should be selected with this relationshipin mind. Make selection of size so that, for anestimatedmodulus, the resonance frequencies measured will fall withinthe range of frequency response of the transducers used.Representative values of Youngs modulus are 10 106psi (69GPa) for vitreou
33、s triaxial porcelains and 32 106psi (220GPa) for 85 % alumina porcelains. Recommended specimensizes are 125 by 15 by 6 mm for bars of rectangular crosssection and 125 by 10 to 12 mm for those of circular crosssection. These specimen sizes should produce a fundamentalflexural resonance frequency in t
34、he range from 1000 to 2000Hz. Specimens shall have a minimum mass of5gtoavoidcoupling effects: any size of specimen that has a suitablelength-to-cross section ratio in terms of frequency response andmeets the mass minimum may be used. Maximum specimensize and mass are determined primarily by the tes
35、t systemsenergy and space capabilities.5.3 Finish specimens using a fine grind, 400 grit or smaller.All surfaces shall be flat and opposite surfaces shall be parallelwithin 0.02 mm.6. Procedure6.1 Procedure A, Room Temperature TestingPosition thespecimen properly (see Figs. 3 and 4). Activate the eq
36、uipmentso that power adequate to excite the specimen is delivered tothe driving transducer. Set the gain of the detector circuit highenough to detect vibration in the specimen and to display it onthe oscilloscope screen with sufficient amplitude to measureaccurately the frequency at which the signal
37、 amplitude ismaximized. Adjust the oscilloscope so that a sharply definedhorizontal baseline exists when the specimen is not excited.Scan frequencies with the audio oscillator until specimenresonance is indicated by a sinusoidal pattern of maximumamplitude on the oscilloscope. Find the fundamental m
38、ode ofvibration in flexure, then find the first overtone in flexure (Note3). Establish definitely the fundamental flexural mode bypositioning the detector at the appropriate nodal position of thespecimen (see Fig. 5). At this point, the amplitude of theresonance signal will decrease to zero. The rat
39、io of the firstovertone frequency to the fundamental frequency will beapproximately 2.70 to 2.75. If a determination of the shearmodulus is to be made, offset the coupling to the transducers sothat the torsional mode of vibration may be detected (see Fig.3). Find the fundamental resonance vibration
40、in this mode.Identify the torsional mode by centering the detector withrespect to the width of the specimen and observing that theamplitude of the resonance signal decreases to zero; if it doesnot, the signal is an overtone of flexure or a spurious frequencygenerated elsewhere in the system. Dimensi
41、ons and weight ofthe specimen may be measured before or after the test.1Cylindrical glass jar2Glass wool3Plastic foam4Vacuum jar5Heater disk6Copper plate7Thermocouple8Sample9Suspension wires10Fill port for liquidFIG. 2 Detail Drawing of Suitable Cryogenic ChamberFIG. 3 Specimen Positioned for Measur
42、ement of Flexural andTorsional Resonance Frequencies Using Thread or Wire Suspen-sionC848 88 (2016)3Measure the dimensions with a micrometer caliper capable ofan accuracy of 60.01 mm; measure the weight with a balancecapable of 610-g accuracy.NOTE 3It is recommended that the first overtone in flexur
43、e bedetermined for both rectangular and cylindrical specimens. This is usefulin establishing the proper identification of the fundamental, particularlywhen spurious frequencies inherent in the system interfere (as, forexample, when greater excitation power and detection sensitivity arerequired for w
44、ork with a specimen that has a poor response). Thefundamental and overtone are properly identified by showing them to bein the correct numerical ratio, and by demonstrating the proper locationsof the nodes for each. Spinner and Tefft recommend using only thefundamental in flexure when computing Youn
45、gs modulus for a rectangu-lar bar because of the approximate nature of Picketts theory. However, forthe nominal size of bar specified, the values ofYoungs modulus computedusing Eq 1 and Eq 2 will agree within 1 %. When the correction factor, T2,is greater than 2 %, Eq 2 should not be used.6.2 Proced
46、ure B, Elevated Temperature TestingDeterminethe mass, dimensions, and frequencies at room temperature inair as outlined in 6.1. Place the specimen in the furnace andadjust the driver-detector system so that all the frequencies tobe measured can be detected without further adjustment.Determine the re
47、sonant frequencies at room temperature in thefurnace cavity with the furnace doors closed, and so forth, aswill be the case at elevated temperatures. Heat the furnace at acontrolled rate that does not exceed 150C/h. Take data at 25intervals or at 15-min intervals as dictated by heating rate andspeci
48、men composition. Follow the change in resonance fre-quencies with time closely to avoid losing the identity of eachfrequency. (The overtone in flexure and the fundamental intorsion may be difficult to differentiate if not followed closely;spurious frequencies inherent in the system may also appear a
49、ttemperatures above 600C using certain types of suspensions,particularly wire.) If desired, data may also be taken oncooling; it must be remembered, however, that high tempera-tures may damage the specimen, by serious warping forexample, making subsequent determinations of doubtful value.6.3 Procedure CCryogenic Temperature TestingDetermine the weight, dimensions, and resonance frequenciesin air at room temperature. Measure the resonance frequenciesat room temperature in the cryogenic chamber. Take thechamber to the minimum temperature desir
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