1、Designation: E 1875 08Standard 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, t
2、he 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 dy-namic elastic properties of elastic materials. Specimen
3、s 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, mass,and mechanical resonant frequencies of a suitable tes
4、t 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. Dynamic Youngs modulus and dynamic shear modulusare used t
5、o 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 method with the understanding thatthe character (volume fra
6、ction, 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 interpreting the test results for composites. Thistest method
7、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 A high-temperature furnace and cryogenic cabinet aredescri
8、bed 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 with a particular geometry andmass. Any specimen with a freque
9、ncy 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 possess if its geometry andmass are within specified toleranc
10、es.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 848, C 1198, and C 1259 may differ from this test method in
11、several 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, andcalculations are consistent with these test methods.1.6 Th
12、e values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.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-pria
13、te safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:1This test method is under the jurisdiction of ASTM Committee E28 onMechanical Testing and is the direct responsibility of Subcommittee E28.04 onUniaxial T
14、esting.Current edition approved Dec. 1, 2008. Published January 2009. Originallyapproved in 1997. Last previous edition approved in 2000 as E1875-001.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStand
15、ards 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.C 215 Test Method for Fundamental Transverse, Longitu-dinal, and Torsional Resonant Frequencies
16、of ConcreteSpecimensC 623 Test Method for Youngs Modulus, Shear Modulus,and Poissons Ratio for Glass and Glass-Ceramics byResonanceC 747 Test Method for Moduli of Elasticity and Fundamen-tal Frequencies of Carbon and Graphite Materials by SonicResonanceC 848 Test Method for Youngs Modulus, Shear Mod
17、ulus,and Poissons Ratio For Ceramic Whitewares by Reso-nanceC 1198 Test Method for Dynamic Youngs Modulus, ShearModulus, and Poissons Ratio for Advanced Ceramics bySonic ResonanceC 1259 Test Method for Dynamic Youngs Modulus, ShearModulus, and Poissons Ratio for Advanced Ceramics byImpulse Excitatio
18、n of VibrationE6 Terminology Relating to Methods of Mechanical Test-ingE 177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE 691 Practice for Conducting an Interlaboratory Study toDetermine the Precision of a Test Method3. Terminology3.1 Definitions:3.1.1 dynamic mechanical mea
19、surement, 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 combinationthereof.3.1.2 elastic limit FL2, nthe greatest stress that amaterial is capable of sustai
20、ning 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 value of theratio of transverse strain to the corresponding axial strainresulting from
21、 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 equation: 5 E/2G! 1 (1)(E 6)3.1.5 proportional limit FL2, nthe greatest stress that amat
22、erial 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 torsionalmodulus.3.1.7 Youngs modulus (E) FL2, nthe elastic modulus intension or compre
23、ssion. (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-nodes. For the fundamen-tal flexure resonance, the anti-nodes are located at the two ends
24、and 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 uniform deformation, that will be eliminated upon removalof the stress, with the bod
25、y 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 oscillations in aslender rod or bar are in a vertical plane normal to the lengthdimension, the v
26、ibrations 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 representative ofthe whole. Practically, as long as the geometrical dimensions ofthe test specime
27、n 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 are the same in all directionsin the material. Materials are considered isotropic on
28、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 having a constant zero displacement, callednodes. For the fundamental flexural resonanc
29、e, 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 inresonance when the imposed frequency is such that theresultant displacements for a given am
30、ount 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 dynamic elastic propertytesting, a specimen whose ratio of length to minimum cross-secti
31、onal 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 the length dimension axis, the vibrationsare said to be in the torsional mode.4. Summa
32、ry 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 through the use of a transducer thattransforms a cyclic electrical signal into a cyclic mec
33、hanicalforce 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 oscilloscope or other means to detectresonance. The resonant frequencies, dimensions, an
34、d mass ofE1875082the 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 measuring moduli.5.1.1 This test method is nondestructive in nature. Onlyminute
35、 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 method it is feasible to performmeasurements at high temperatures, where delayed
36、 elastic andcreep effects would invalidate modulus measurements calcu-lated from static loading.5.2 This test method is suitable for detecting whether amaterial meets specifications, if cognizance is given to oneimportant fact in materials are often sensitive to thermalhistory. Therefore, the therma
37、l history of a test specimen mustbe considered in comparing experimental values of moduli toreference or standard values. Specimen descriptions shouldinclude any specific thermal treatments that the specimens havereceived.6. Apparatus6.1 The test apparatus is shown in Fig. 1. It consists of avariabl
38、e-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 frequency meter (preferably digital) monitors the audiooscillator output to provide an accurate frequency determina-
39、tion. A suitable suspension-coupling system supports the testspecimen. Another transducer acts to detect mechanical vibra-tion in 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-t
40、er, or oscilloscope. An oscilloscope is recommended becauseit enables the operator to positively identify resonances,including higher 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 oscillosco
41、pe. Iftemperature-dependent data are desired, a suitable furnace orcryogenic chamber is used. Details of the equipment are asfollows: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 set
42、ting.6.3 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.6.4 Transducers Two are required; one used as a drivermay be a speaker of the tweeter type or a magnetic cutting heador other s
43、imilar 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. An electromagnetic couplingsystem with an atta
44、ched metal foil may also be used, with dueconsideration for effects of the foil on the natural vibration ofthe test bar. The frequency 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 det
45、ector circuit shall be imped-ance matched with the type of detector transducer selected andshall serve as a prescope amplifier.6.6 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.
46、6.8 FurnaceIf data at an elevated temperature are desired,a furnace shall be used that is capable of controlled heating andcooling. 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 intesti
47、ng. It is recommended that an independent thermocouplebe placed in close proximity to (within 5 min), but nottouching, the center 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
48、 be capable ofcontrolled heating/cooling, frost-free and uniform in tempera-ture within 65C over the length of the specimen at anyselected 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),
49、 but nottouching, the center of the specimen to accurately measuretemperature during heating and cooling.6.10 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 cryogenic and high-temperature testing. (See Fig.1 and Fig. 3.) Common cotton thread, silica-glass fiber thread,oxidation-resistant nickel (or platinum) alloy wire, or p
