1、Designation: C 848 88 (Reapproved 2006)Standard Test Method forYoungs Modulus, Shear Modulus, and Poissons Ratio ForCeramic Whitewares by Resonance1This standard is issued under the fixed designation C 848; the number immediately following the designation indicates the year oforiginal adoption or, i
2、n the case of revision, the year 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 the determination of the elasticproperties of ceramic whi
3、teware 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 frequen
4、cies 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
5、 Poissons ratio, the factor oflateral contraction.1.2 All ceramic whiteware materials that are elastic, homo-geneous, and isotropic may be tested by this test method.2Thistest method is not satisfactory for specimens that have cracksor voids that represent inhomogeneities in the material; neitheris
6、it satisfactory when these materials cannot be prepared in asuitable 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 stre
7、ss, 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 cryoge
8、nic 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
9、 density.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 den
10、sity 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 limi
11、tations 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 initialelectric
12、al signal 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 th
13、especimen 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
14、possibility of fracture.1This test method is under the jurisdiction ofASTM Committee C21 on CeramicWhitewares and Related Products and is the direct responsibility of SubcommitteeC21.03 on Methods for Whitewares and Environmental Concerns.Current edition approved Feb. 15, 2006. Published February 20
15、06. Originallyapproved in 1976. Last previous edition approved in 1999 as C 848 88 (1999).2Spinner, S., and Tefft, W. E., “A Method for Determining MechanicalResonance Frequencies and for Calculating Elastic Moduli from These Frequen-cies,” Proceedings, ASTM, 1961, pp. 12211238.1Copyright ASTM Inter
16、national, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.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 effec
17、ts proceed on a much-shortenedtime scale.3.2 This test method is suitable 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 bef
18、ore the moduli can be consideredin 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-dal voltage,
19、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 transducer
20、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 of theosci
21、lloscope. 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 for any given
22、 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 heador othe
23、r 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 thetransducer sh
24、all 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 any model sui
25、tablefor general laboratory work.4.7 Frequency Counter, shall be able to measure frequen-cies to 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 beunifor
26、m 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, andFIG. 1 Block Diagram of ApparatusC 848 88 (2006)2uniform in temperature within 65C over the le
27、ngth of thespecimen at any selected temperature. 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
28、 thread, silica glass fiber thread,Nichrome, 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 thetransducer. If specimen supports o
29、f other than the suspensiontype are used, they shall meet the same general specifications.5. Test Specimens5.1 Prepare 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 experimenta
30、l difficulties in obtaining torsional resonancefrequencies for a cylindrical specimen usually preclude its usein determining 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 Resonan
31、ce frequencies for a given specimen are func-tions of the bar dimensions as well as its density and modulus;therefore, 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
32、frequency response of the transducers used.Representative values of Youngs modulus are 10 3 106psi(69 GPa) for vitreous triaxial porcelains and 32 3 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 m
33、m for those of circular crosssection. These specimen sizes should produce a fundamentalflexural resonance frequency in the 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 fre
34、quency response andmeets the mass minimum may be used. Maximum specimensize and mass are determined primarily by the test 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
35、.6. Procedure6.1 Procedure A, Room Temperature TestingPosition thespecimen properly (see Figs. 3 and 4). Activate the equipmentso 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
36、to display it onthe oscilloscope screen with sufficient amplitude to measureaccurately the frequency at which the signal amplitude ismaximized. Adjust the oscilloscope so that a sharply definedhorizontal baseline exists when the specimen is not excited.Scan frequencies with the audio oscillator unti
37、l specimenresonance is indicated by a sinusoidal pattern of maximumamplitude on the oscilloscope. Find the fundamental mode ofvibration in flexure, then find the first overtone in flexure (Note3). Establish definitely the fundamental flexural mode by3Smith, R. E., and Hagy, H. E., “A Low Temperature
38、 Sonic ResonanceApparatus for Determining Elastic Properties of Solids,” Internal Report 2195,Corning Glass Works, April 1961.1Cylindrical glass jar2Glass wool3Plastic foam4Vacuum jar5Heater disk6Copper plate7Thermocouple8Sample9Suspension wires10Fill port for liquidFIG. 2 Detail Drawing of Suitable
39、 Cryogenic ChamberFIG. 3 Specimen Positioned for Measurement of Flexural andTorsional Resonance Frequencies Using Thread or WireSuspensionC 848 88 (2006)3positioning the detector at the appropriate nodal position of thespecimen (see Fig. 5). At this point, the amplitude of theresonance signal will d
40、ecrease to zero. The ratio 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 fundamen
41、tal resonance vibration 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 elsewher
42、e in the system. Dimensions and weight ofthe specimen may be measured before or after the test.Measure 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 flexure bed
43、etermined 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 work w
44、ith 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 Youngs mo
45、dulus for a rectangu-lar bar because of the approximate nature of Picketts theory. However, forthe nominal size of bar specified, the values of Youngs moduluscomputed using Eq 1 and Eq 2 will agree within 1 %. When the correctionfactor, T2, is greater than 2 %, Eq 2 should not be used.6.2 Procedure
46、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 resona
47、nt 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 andspecimen
48、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 attem
49、peratures 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 desired (Note
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