1、Designation: E 1875 00e1Standard Test Method forDynamic Youngs Modulus, Shear Modulus, and PoissonsRatio by Sonic Resonance1This standard is issued under the fixed designation E 1875; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision,
2、 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.e1NOTEEquation 13 was editorially revised in March 2002.1. Scope1.1 This test method covers the determination of the
3、 dy-namic elastic properties of elastic materials. Specimens ofthese materials possess specific mechanical resonant frequen-cies that are determined by the elastic modulus, mass, andgeometry of the test specimen. Therefore, the dynamic elasticproperties of a material can be computed if the geometry,
4、 mass,and mechanical resonant frequencies of a suitable test speci-men of that material can be measured. Dynamic Youngsmodulus is determined using the resonant frequency in theflexural mode of vibration. The dynamic shear modulus, ormodulus of rigidity, is found using torsional resonant vibra-tions.
5、 Dynamic Youngs modulus and dynamic shear modulusare used to compute Poissons ratio.1.2 This test method is specifically appropriate for materialsthat are elastic, homogeneous, and isotropic (1).2Materials ofa composite character (particulate, whisker, or fiber reinforced)may be tested by this test
6、method with the understanding thatthe character (volume fraction, size, morphology, distribution,orientation, elastic properties, and interfacial bonding) of thereinforcement in the test specimen will have a direct effect onthe elastic properties. These reinforcement effects must beconsidered in int
7、erpreting the test results for composites. Thistest method is not satisfactory for specimens that have cracksor voids that are major discontinuities in the specimen. Neitheris the test method satisfactory when these materials cannot befabricated in a uniform rectangular or circular cross section.1.3
8、 A high-temperature furnace and cryogenic cabinet aredescribed for measuring the dynamic elastic moduli as afunction of temperature from 195 to 1200C.1.4 Modification of this test method for use in qualitycontrol is possible. A range of acceptable resonant frequenciesis determined for a specimen wit
9、h a particular geometry andmass. Any specimen with a frequency response falling outsidethis frequency range is rejected. The actual modulus of eachspecimen need not be determined as long as the limits of theselected frequency range are known to include the resonantfrequency that the specimen must po
10、ssess if its geometry andmass are within specified tolerances.1.5 There are material specific ASTM standards that coverthe determination of resonance frequencies and elastic proper-ties of specific materials by sonic resonance or by impulseexcitation of vibration. Test Methods C 215, C 623, C 747,C
11、848, C 1198, and C 1259 may differ from this test method inseveral areas (for example; sample size, dimensional toler-ances, sample preparation). The testing of these materials shallbe done in compliance with these material specific standards.Where possible, the procedures, sample specifications, an
12、dcalculations are consistent with these test methods.1.6 The values stated in SI units are regarded as thestandard.1.7 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
13、safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:C 215 Test Method for Fundamental Transverse, Longitu-dinal and Torsional Frequencies of Concrete Specimens2C 623 Test Method for Youngs Modulus, Shear Modulu
14、s,and Poissons Ratio for Glass and Glass-Ceramics byResonance3C 747 Test Method for Moduli of Elasticity and Fundamen-tal Frequencies of Carbon and Graphite Materials by SonicResonance4C 848 Test Method for Dynamic Youngs Modulus, ShearModulus, and Poissons Ratio for Ceramic Whitewares byResonance3C
15、 1198 Test Method for Dynamic Youngs Cynamic Modu-lus, Shear Modulus and Poissons Ratio for Advanced1This test method is under the jurisdiction of ASTM Committee E28 onMechanical Testing and is the direct responsibility of Subcommittee E28.04 onUniaxial Testing.Current edition approved Oct. 10, 2000
16、. Published January 2001.Originally published as E1875-97. Last previous edition E187597.2Annual Book of ASTM Standards, Vol 04.02.3Annual Book of ASTM Standards, Vol 15.02.4Annual Book of ASTM Standards, Vol 15.01.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken,
17、 PA 19428-2959, United States.Ceramics by Sonic Resonance4C 1259 Test Method for Dynamic Youngs Modulus, ShearModulus and Poissons Ratio for Advanced Ceramics byImpulse Excitation of Vibration4E 6 Terminology Relating to Methods of Mechanical Test-ing5E 177 Practice for Use of the Terms Precision an
18、d Bias inASTM Test Methods63. Terminology3.1 Definitions:3.1.1 dynamic mechanical measurement, n a technique inwhich either the modulus or damping, or both, of a substanceunder oscillatory applied force or displacement is measured asa function of temperature, frequency, or time, or a combinationther
19、eof.3.1.2 elastic limit FL2, nthe greatest stress that amaterial is capable of sustaining without permanent strainremaining upon complete release of the stress. (E 63.1.3 elastic modulus FL2, nthe ratio of stress to strainbelow the proportional limit. (E 6)3.1.4 Poissons ratio () nd, nthe absolute v
20、alue of theratio of transverse strain to the corresponding axial strainresulting from uniformly distributed axial stress below theproportional limit of the material.3.1.4.1 DiscussionIn isotropic materials Youngs modu-lus ( E), shear modulus (G), and Poissons ratio () are relatedby the following equ
21、ation: 5 E/2G! 1 (1)(E 6)3.1.5 proportional limit FL2, nthe greatest stress that amaterial is capable of sustaining without deviation fromproportionality of stress to strain (Hookes law). (E 6)3.1.6 shear modulus (G) FL2, nthe elastic modulus inshear or torsion. Also called modulus of rigidity or to
22、rsionalmodulus.3.1.7 Youngs modulus (E) FL2, nthe elastic modulus intension or compression. (E 6)3.2 Definitions of Terms Specific to This Standard:3.2.1 anti-nodes, nan unconstrained slender rod or bar inresonance contains two or more locations that have localmaximum displacements, called anti-node
23、s. For the fundamen-tal flexure resonance, the anti-nodes are located at the two endsand the center of the specimen.3.2.2 elastic, adjthe property of a material such that anapplication of stress within the elastic limit of that materialmaking up the body being stressed will cause an instantaneousand
24、 uniform deformation, that will be eliminated upon removalof the stress, with the body returning instantly to its originalsize and shape without energy loss. Most elastic materialsconform to this definition well enough to make this resonancetest valid.3.2.3 flexural vibrations, nwhen the oscillation
25、s in aslender rod or bar are in a vertical plane normal to the lengthdimension, the vibrations are said to be in the flexural mode.3.2.4 homogeneous, adjthe condition of a specimen suchthat the composition and density are uniform, such that anysmaller specimen taken from the original is representati
26、ve ofthe whole. Practically, as long as the geometrical dimensions ofthe test specimen are large with respect to the size of individualgrains, crystals, or components, the body can be consideredhomogeneous.3.2.5 isotropic, adjthe condition of a specimen such thatthe values of the elastic properties
27、are the same in all directionsin the material. Materials are considered isotropic on a mac-roscopic scale, if they are homogeneous and there is a randomdistribution and orientation of phases, crystallites, and compo-nents.3.2.6 nodes, nslender rod or bar in resonance contains oneor more locations ha
28、ving a constant zero displacement, callednodes. For the fundamental flexural resonance, the nodes arelocated at 0.224 L from each end, where L is the length of thespecimen.3.2.7 resonance, nslender rod or bar driven into one of themodes of vibration described in 3.2.3 or 3.2.9 is said to be inresona
29、nce when the imposed frequency is such that theresultant displacements for a given amount of driving force areat a maximum. The resonant frequencies are natural vibrationfrequencies that are determined by the elastic modulus, mass,and dimensions of the test specimen.3.2.8 slender rod or bar, nin dyn
30、amic elastic propertytesting, a specimen whose ratio of length to minimum cross-sectional dimension is at least five and preferably in the rangefrom 20 to 25.3.2.9 torsional vibrations, nwhen the oscillations in eachcross-sectional plane of a slender rod or bar are such that theplane twists around t
31、he length dimension axis, the vibrationsare said to be in the torsional mode.4. Summary of Test Method4.1 This test method measures the resonant frequencies oftest specimens of suitable geometry by exciting them atcontinuously variable frequencies. Mechanical excitation ofthe bars is provided throug
32、h the use of a transducer thattransforms a cyclic electrical signal into a cyclic mechanicalforce on the specimen.Asecond transducer senses the resultingmechanical vibrations of the specimen and transforms theminto an electrical signal. The amplitude and frequency of thesignal are measured by an osc
33、illoscope or other means to detectresonance. The resonant frequencies, dimensions, and mass ofthe specimen are used to calculate dynamic Youngs modulusand dynamic shear modulus.5. Significance and Use5.1 This test method has advantages in certain respects overthe use of static loading systems for me
34、asuring moduli.5.1.1 This test method is nondestructive in nature. Onlyminute stresses are applied to the specimen, thus minimizingthe possibility of fracture.5.1.2 The period of time during which measurement stressis applied and removed is of the order of hundreds ofmicroseconds. With this test met
35、hod it is feasible to performmeasurements at high temperatures, where delayed elastic and5Annual Book of ASTM Standards, Vol 03.01.6Annual Book of ASTM Standards, Vol 14.02.E187500e12creep effects would invalidate modulus measurements calcu-lated from static loading.5.2 This test method is suitable
36、for detecting whether amaterial meets specifications, if cognizance is given to oneimportant fact in materials are often sensitive to thermalhistory. Therefore, the thermal history of a test specimen mustbe considered in comparing experimental values of moduli toreference or standard values. Specime
37、n descriptions shouldinclude any specific thermal treatments that the specimens havereceived.6. Apparatus6.1 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
38、 electrical signal to a mechanical driving vibration.A frequency meter (preferably digital) monitors the audiooscillator output to provide an accurate frequency determina-tion. A suitable suspension-coupling system supports the testspecimen. Another transducer acts to detect mechanical vibra-tion in
39、 the specimen and to convert it into an electrical signalthat is passed through an amplifier and displayed on anindicating meter. The meter may be a voltmeter, microamme-ter, or oscilloscope. An oscilloscope is recommended becauseit enables the operator to positively identify resonances,including hi
40、gher order harmonics, by Lissajous figure analysis.If a Lissajous figure is desired, the output of the oscillator isalso coupled to the horizontal plates of the oscilloscope. Iftemperature-dependent data are desired, a suitable furnace orcryogenic chamber is used. Details of the equipment are asfoll
41、ows:6.2 Audio Oscillator, having a continuously variable fre-quency output from about 100 Hz to at least 30 kHz. Frequencydrift shall not exceed 1 Hz/min for any given setting.6.3 Audio Amplifier, having a power output sufficient toensure that the type of transducer used can excite any specimenthe m
42、ass of which falls within a specified range.6.4 Transducers Two 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. Theother transducer, used
43、as a detector, may be a crystal ormagnetic reluctance type of phonograph cartridge.Acapacitivepickup may be used if desired. An electromagnetic couplingsystem with an attached metal foil may also be used, with dueconsideration for effects of the foil on the natural vibration ofthe test bar. The freq
44、uency response of the transducer acrossthe frequency range of interest shall have at least a 6.5 kHzbandwidth before 3 dB power loss occurs.6.5 Power Amplifier, in the detector circuit shall be imped-ance matched with the type of detector transducer selected andshall serve as a prescope amplifier.6.
45、6 Cathode-Ray Oscilloscope, any model suitable for gen-eral laboratory work.6.7 Frequency Counter, preferably digital, shall be able tomeasure frequencies to within 61 Hz.6.8 FurnaceIf data at an elevated temperature are desired,a furnace shall be used that is capable of controlled heating andcoolin
46、g. It shall have a specimen zone large enough for thespecimen to be uniform in temperature within 65C along itslength through the range of temperatures encountered intesting. It is recommended that an independent thermocouplebe placed in close proximity to (within 5 min), but nottouching, the center
47、 of the specimen to accurately measuretemperature during heating and cooling.6.9 Cryogenic ChamberFor data at cryogenic tempera-tures, any chamber shall suffice that shall be capable ofcontrolled heating/cooling, frost-free and uniform in tempera-ture within 65C over the length of the specimen at an
48、yselected temperature.Asuitable cryogenic chamber is shown inFig. 2 (2). It is recommended that an independent thermo-couple be placed in close proximity to (within 5 mm), but nottouching, the center of the specimen to accurately measuretemperature during heating and cooling.FIG. 1 Block Diagram of
49、a Typical Test ApparatusNOTE 1Legend:1 = Cylindrical glass jar2 = Glass wool3 = Plastic foam4 = Vacuum jar5 = Heater disk6 = Copper plate7 = Thermocouple8 = Sample9 = Suspension wires10 = Fill port for liquidFIG. 2 Detail Drawing of a Typical Cryogenic ChamberE187500e136.10 Specimen SuspensionAny method of specimen sus-pension shall be used that is adequate for the temperaturesencountered in testing and that allows the specimen to vibratewithout significant restriction. Thread suspension is the systemof choice for cryo
