1、Designation: C 623 92 (Reapproved 2005)Standard Test Method forYoungs Modulus, Shear Modulus, and Poissons Ratio forGlass and Glass-Ceramics by Resonance1This standard is issued under the fixed designation C 623; the number immediately following the designation indicates the year oforiginal adoption
2、 or, in 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 glass
3、 and glass-ceramic materials. Specimens ofthese materials possess specific mechanical resonance frequen-cies which are defined by the elastic moduli, density, andgeometry of the test specimen. Therefore the elastic propertiesof a material can be computed if the geometry, density, andmechanical reson
4、ance frequencies of a suitable test specimenof that material can be measured. Youngs modulus is deter-mined using the resonance frequency in the flexural mode ofvibration. The shear modulus, or modulus of rigidity, is foundusing torsional resonance vibrations. Youngs modulus andshear modulus are use
5、d to compute Poissons ratio, the factorof lateral contraction.1.2 All glass and glass-ceramic materials that are elastic,homogeneous, and isotropic may be tested by this test method.2The test method is not satisfactory for specimens that havecracks or voids that represent inhomogeneities in the mate
6、rial;neither is it satisfactory 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 re
7、movalof the stress, with the body returning instantly to its original size and shapewithout an energy loss. Glass and glass-ceramic 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 mate
8、rial. Glass is isotropic and glass-ceramics are usuallyso on a macroscopic scale, because of random distribution and orientationof crystallites.1.3 A cryogenic cabinet and high-temperature furnace aredescribed for measuring the elastic moduli as a function oftemperature from 195C to 1200C.1.4 Modifi
9、cation of the test for use in quality control ispossible. A range of acceptable resonance frequencies isdetermined for a piece with a particular geometry and density.Any specimen with a frequency response falling outside thisfrequency range is rejected. The actual modulus of each pieceneed not be de
10、termined 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 arewithin specified tolerances.1.5 This standard does not purport to address all of thesafety concerns, if any, associated with its use. I
11、t 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. Summary of Test Method2.1 This test method measures the resonance frequencies oftest bars of suitable geometry by excit
12、ing them at continuouslyvariable frequencies. Mechanical excitation of the specimen isprovided through use of a transducer that transforms an initialelectrical signal into a mechanical vibration. Another trans-ducer senses the resulting mechanical vibrations of the speci-men and transforms them into
13、 an electrical signal that can bedisplayed on the screen of an oscilloscope to detect resonance.The reasonance frequencies, the dimensions, and the mass ofthe specimen are used to calculate Youngs modulus and theshear modulus.3. Significance and Use3.1 This test system has advantages in certain resp
14、ects overthe use of static loading systems in the measurement of glassand glass-ceramics:3.1.1 Only minute stresses are applied to the specimen, thusminimizing the possibility of fracture.3.1.2 The period of time during which stress is applied andremoved is of the order of hundreds of microseconds,
15、makingit feasible to perform measurements at temperatures wheredelayed elastic and creep effects proceed on a much-shortenedtime scale, as in the transformation range of glass, for instance.3.2 The test is suitable for detecting whether a materialmeets specifications, if cognizance is given to one i
16、mportantfact: glass and glass-ceramic materials are sensitive to thermal1This test method is under the jurisdiction of ASTM Committee C14 on Glassand Glass Products and is the direct responsibility of Subcommittee C14.04 onPhysical and Mechanical Properties.Current edition approved Sept. 1, 2005. Pu
17、blished October 2005. Originallyapproved in 1969. Last previous edition approved in 2000 as C 623 92 (2000).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. 12211238.1Co
18、pyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.history. Therefore the thermal history of a test specimen mustbe known before the moduli can be considered in terms ofspecified values. Material specifications should include aspecific the
19、rmal 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, and a power amplifier and suitable transducer toconvert the electrical signal to a mechanical driving vibration.A
20、frequency meter monitors the audio oscillator output toprovide an accurate frequency determination. A suitablesuspension-coupling system cradles the test specimen, andanother transducer acts to detect mechanical resonance in thespecimen and to convert it into an electrical signal which ispassed thro
21、ugh 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 theoscilloscope. If temperature-dependent data are desired, asuitable furnace or cryogenic chamber is used. Details of th
22、eequipment are as follows:4.2 Audio Oscillator, having a continuously variable fre-quency output from about 100 Hz to at least 20 kHz. Frequencydrift shall not exceed 1 Hz/min for any given setting.4.3 Audio Amplifier, having a power output sufficient toensure that the type of transducer used can ex
23、cite 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 other similar device, depending on the type of couplingchosen for use between the transducer and the specimen. Theo
24、ther 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 shall be as good as possible with at least a 6.5-kHzbandwidth before 3-dB power loss occurs.4.5 Power Amplifier,
25、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 suitablefor general laboratory work.4.7 Frequency Counter, shall be able to measure frequen-cies to within 61 Hz.4
26、.8 If data at elevated temperature 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 beuniform in temperature within 65C throughout the range oftemperatures encountered in testing.4.9 For data at cryogenic
27、 temperatures, any chamber shallsuffice that shall be capable of controlled heating, frost-free,and uniform in temperature within 65C over the length of thespecimen at any selected temperature. A suitable cryogenicchamber3is shown in Fig. 2.4.10 Any method of specimen suspension shall be used thatsh
28、all be adequate for the temperatures encountered in testingand that shall allow the specimen to vibrate without significantrestriction. Common cotton thread, silica glass fiber thread,Nichrome, or platinum wire may be used. If metal wiresuspension is used in the furnace, coupling characteristics wil
29、lbe 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 ResonanceApparatus for Determining Elastic Properties of Solids,” Internal Report 2195,Corning Glass Works, April, 1961.FIG. 1 B
30、lock Diagram of ApparatusC 623 92 (2005)2transducer. If specimen supports of other than the suspensiontype are used, they shall meet the same general specifications.5. Test Specimen5.1 The specimens shall be prepared so that they are eitherrectangular or circular in cross section. Either geometry ca
31、n beused to measure both Youngs modulus and shear modulus.However, great experimental difficulties in obtaining torsionalresonance frequencies for a cylindrical specimen usually pre-clude its use in determining shear modulus, although theequations for computing shear modulus with a cylindricalspecim
32、en are both simpler and more accurate than those usedwith 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;therefore, dimensions should be selected with this relationshipin mind. Selection of size shall be made so
33、that, for anestimated modulus, the resonance frequencies measured willfall within the range of frequency response of the transducersused. Representative values of Youngs modulus are 70 3 104kgf/cm2(69 GPa) for glass and 100 3 104kgf/cm2(98 GPa)for glass-ceramics. Recommended specimen sizes are 120 b
34、y25 by 3 mm for bars of rectangular cross section, and 120 by4 mm for those of circular cross section. These specimen sizesshould produce a fundamental flexural resonance frequency inthe range from 1000 to 2000 Hz. Specimens shall have aminimum mass of 5 g to avoid coupling effects; any size ofspeci
35、men that has a suitable length-to-cross section ratio interms of frequency response and meets the mass minimum maybe used. Maximum specimen size and mass are determinedprimarily by the test systems energy and space capabilities.5.3 Specimens shall be finished using a fine grind 400-gritor smaller. A
36、ll surfaces shall be flat and opposite surfaces shallbe parallel within 0.02 mm.6. Procedure6.1 Procedure ARoom Temperature TestingPosition thespecimen properly (see Fig. 3 and Fig. 4). Activate theequipment so that power adequate to excite the specimen isdelivered to the driving transducer. Set the
37、 gain of the detectorcircuit high enough to detect vibration in the specimen and todisplay it on the oscilloscope screen with sufficient amplitudeto measure accurately the frequency at which the signalamplitude is maximized. Adjust the oscilloscope so that asharply defined horizontal baseline exists
38、 when the specimen isnot excited. Scan frequencies with the audio oscillator untilspecimen resonance is indicated by a sinusoidal pattern ofmaximum amplitude on the oscilloscope. Find the fundamentalmode of vibration in flexure, then find the first overtone inflexture (Note 3). Establish definitely
39、the fundamental flexuralmode by positioning the detector at the appropriate nodalposition of the specimen (see Fig. 5). At this point theamplitude of the resonance signal will decrease to zero. Theratio of the first overtone frequency to the fundamentalfrequency will be approximately 2.70 to 2.75. I
40、f a determina-tion of the shear modulus is to be made, offset the coupling tothe transducers so that the torsional mode of vibration may bedetected (see Fig. 3). Find the fundamental resonance vibrationin this mode. Identify the torsional mode by centering thedetector with respect to the width of th
41、e specimen andobserving that the amplitude of the resonance signal decreasesto zero; if it does not, the signal is an overtone of flexure or aspurious frequency generated elsewhere in the system. Dimen-sions and weight of the specimen may be measured before orafter the test. Measure the dimensions w
42、ith a micrometer1Cylindrical glass jar2Glass wool3Plastic foam4Vacuum jar5Heater disk6Copper plate7Thermocouple8Sample9Suspension wires10Fill port for liquidFIG. 2 Detail Drawing of Suitable Cryogenic ChamberFIG. 3 Specimen Positioned for Measurement of Flexural andTorsional Resonance Frequencies Us
43、ing Thread or WireSuspensionC 623 92 (2005)3caliper capable of an accuracy of 60.01 mm; measure theweight with a balance capable of 610 mg accuracy.NOTE 3It is recommended that the first overtone in flexure bedetermined for both rectangular and cylindrical specimens. This is usefulin establishing th
44、e 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 with a specimen that has a poor response). Thefundamental and overtone are properly identif
45、ied by showing them to bein the correct numerical ratio, and by demonstrating the proper locationsof the nodes for each. Spinner and Tefft recommended using only thefundamental in flexure when computing Youngs modulus for a rectangu-lar bar because of the approximate nature of Picketts theory. Howev
46、er, 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 BElevated Temperature TestingDetermine the mass, dimensions, and frequencies at roomtemp
47、erature in air as outlined in 6.1. Place the specimen in thefurnace and adjust the driver-detector system so that all thefrequencies to be measured can be detected without furtheradjustment. Determine the resonant frequencies at room tem-perature in the furnace cavity with the furnace doors closed,e
48、tc., as will be the case at elevated temperatures. Heat thefurnace at a controlled rate that does not exceed 150C/h. Takedata at 25 intervals or at 15-min intervals as dictated byheating rate and specimen composition. Follow the change inresonance frequencies with time closely to avoid losing theide
49、ntity of each frequency. (The overtone in flexure and thefundamental in torsion may be difficult to differentiate if notfollowed closely; spurious frequencies inherent in the systemmay also appear at temperatures above 600C using certaintypes of suspensions, particularly wire.) If desired, data mayalso be taken on cooling; it must be remembered, however, thathigh temperatures may damage the specimen, by seriouswarping for example, making subsequent determinations ofdoubtful value.6.3 Procedure CCryogenic Temperature TestingDetermine the weigh
