1、Designation: E1875 13Standard Test Method forDynamic Youngs Modulus, Shear Modulus, and PoissonsRatio by Sonic Resonance1This standard is issued under the fixed designation E1875; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the
2、 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. Scope*1.1 This test method covers the determination of the dy-namic elastic properties of elastic materials. Specimens
3、 ofthese materials possess specific mechanical resonant frequen-cies that are determined by the modulus of elasticity, 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 suitabl
4、e 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. Dynamic Youngs modulus and dynamic shear modulusare u
5、sed 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 method with the understanding thatthe character (volum
6、e 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 interpreting the test results for composites. Thistest me
7、thod 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 ared
8、escribed 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 f
9、requency 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 tol
10、erances.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 C215, C623, C747, C848,C1198, and C1259 may differ from this test method in
11、severalareas (for example; sample size, dimensional tolerances,sample preparation). The testing of these materials shall bedone in compliance with these material specific standards.Where possible, the procedures, sample specifications, andcalculations are consistent with these test methods.1.6 The v
12、alues 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-priate
13、safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:3C215 Test Method for Fundamental Transverse,Longitudinal, and Torsional Resonant Frequencies ofConcrete SpecimensC623 Test Method for Youngs Modulus, Shear M
14、odulus,and Poissons Ratio for Glass and Glass-Ceramics byResonanceC747 Test Method for Moduli of Elasticity and FundamentalFrequencies of Carbon and Graphite Materials by SonicResonance1This test method is under the jurisdiction of ASTM Committee E28 onMechanical Testing and is the direct responsibi
15、lity of Subcommittee E28.04 onUniaxial Testing.Current edition approved Nov. 1, 2013. Published May 2014. Originallyapproved in 1997. Last previous edition approved in 2008 as E1875-08. DOI:10.1520/E1875-13.2The boldface numbers in parentheses refer to a list of references at the end ofthis standard
16、.3For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.*A Summary of Changes section appears at the end of this sta
17、ndardCopyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1C848 Test Method for Youngs Modulus, Shear Modulus,and Poissons Ratio For Ceramic Whitewares by Reso-nanceC1198 Test Method for Dynamic Youngs Modulus, ShearModulus, and Poissons Ra
18、tio for Advanced Ceramics bySonic ResonanceC1259 Test Method for Dynamic Youngs Modulus, ShearModulus, and Poissons Ratio for Advanced Ceramics byImpulse Excitation of VibrationE6 Terminology Relating to Methods of Mechanical TestingE177 Practice for Use of the Terms Precision and Bias inASTM Test M
19、ethodsE691 Practice for Conducting an Interlaboratory Study toDetermine the Precision of a Test Method3. Terminology3.1 Definitions:Terms common to mechanical testing.3.1.1 dynamic mechanical measurement, n a technique inwhich either the modulus or damping, or both, of a substanceunder oscillatory a
20、pplied 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 sustaining without permanent strainremaining upon complete release of the stress.3.1.2.1 DiscussionDue to practi
21、cal considerations in de-termining the elastic limit, measurements of strain using asmall force, rather than zero force, are usually taken as theinitial and final reference. (E6)3.1.3 modulus of elasticity FL2,nthe ratio of stress tocorresponding strain below the proportional limit.3.1.3.1 Discussio
22、nThe stress-strain relationships of manymaterials do not conform to Hookes law throughout the elasticrange, but deviate therefrom even at stresses well below theelastic limit. For such materials, the slope of either the tangentto the stress-strain curve at the origin or at a low stress, thesecant dr
23、awn from the origin to any specified point on thestress-strain curve, or the chord connecting any two specifiedpoints on the stress-strain curve is usually taken to be the“modulus of elasticity.” In these cases, the modulus should bedesignated as the “tangent modulus,” the “secant modulus,” orthe “c
24、hord modulus,” and the point or points on the stress-strain curve described. Thus, for materials where the stress-strain relationship is curvilinear rather than linear, one of thefour following terms may be used:(a) initial tangent modulus FL2, nthe slope of thestress-strain curve at the origin.(b)
25、tangent modulus FL2, nthe slope of the stress-strain curve at any specified stress or strain.(c ) secant modulus FL2, nthe slope of the secantdrawn from the origin to any specified point on the stress-strain curve.(d) chord modulus FL2, nthe slope of the chorddrawn between any two specified points o
26、n the stress-straincurve below the elastic limit of the material.3.1.3.2 DiscussionModulus of elasticity, like stress, isexpressed in force per unit of area (pounds per square inch,etc.).3.1.4 Poissons ratio, ,nthe negative of the ratio oftransverse strain to the corresponding axial strain resulting
27、from an axial stress below the proportional limit of thematerial.3.1.4.1 DiscussionPoissons ratio may be negative forsome materials, for example, a tensile transverse strain willresult from a tensile axial strain.3.1.4.2 DiscussionPoissons ratio will have more than onevalue if the material is not is
28、otropic. (E6)3.1.5 proportional limit FL2 ,nthe greatest stress that amaterial is capable of sustaining without deviation fromproportionality of stress to strain (Hookes law).3.1.5.1 DiscussionMany experiments have shown thatvalues observed for the proportional limit vary greatly with thesensitivity
29、 and accuracy of the testing equipment, eccentricityof loading, the scale to which the stress-strain diagram isplotted, and other factors. When determination of proportionallimit is required, the procedure and the sensitivity of the testequipment should be specified. (E6)3.1.6 shear modulus (G) FL2,
30、nthe ratio of shear stressto corresponding shear strain below the proportional limit, alsocalled torsional modulus and modulus of rigidity.3.1.6.1 DiscussionThe value of the shear modulus maydepend on the direction in which it is measured if the materialis not isotropic. Wood, many plastics and cert
31、ain metals aremarkedly anisotropic. Deviations from isotropy should besuspected if the shear modulus differs from that determined bysubstituting independently measured values of Youngsmodulus, E, and Poissons ratio, , in the relation:G 5 E/211!#3.1.6.2 DiscussionIn general, it is advisable in report
32、ingvalues of shear modulus to state the range of stress over whichit is measured.3.1.7 Youngs modulus (E) FL2 ,nthe ratio of tensile orcompressive stress to corresponding strain below the propor-tional limit of the material. (E6)3.2 Definitions of Terms Specific to This Standard:3.2.1 anti-nodes, nt
33、wo or more locations in an uncon-strained slender rod or bar in resonance that have localmaximum displacements.3.2.1.1 DiscussionFor the fundamental flexure resonance,the anti-nodes are located at the two ends and the center of thespecimen.3.2.2 elastic, adjthe property of a material such that anapp
34、lication 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 body returning instantly to its originalsize and shape without energy loss.3.2.2.1 DiscussionMo
35、st elastic materials conform to thisdefinition well enough to make this resonance test valid.3.2.3 flexural vibrations, noscillations that occur in aslender rod or bar in a vertical plane normal to the lengthdimension.E1875 1323.2.4 homogeneous, adjthe condition of a specimen suchthat the compositio
36、n and density are uniform, such that anysmaller specimen taken from the original is representative ofthe whole.3.2.4.1 DiscussionPractically, as long as the geometricaldimensions of the test specimen are large with respect to thesize of individual grains, crystals, or components, the body canbe cons
37、idered homogeneous.3.2.5 isotropic, adjthe condition of a specimen such thatthe values of the elastic properties are the same in all directionsin the material.3.2.5.1 DiscussionMaterials are considered isotropic on amacroscopic scale, if they are homogeneous and there is arandom distribution and ori
38、entation of phases, crystallites, andcomponents.3.2.6 nodes, none or more locations of a slender rod or barin resonance that have a constant zero displacement.3.2.6.1 DiscussionFor the fundamental flexuralresonance, the nodes are located at 0.224 L from each end,where L is the length of the specimen
39、.3.2.7 resonance, nstate of slender rod or bar driven intoone of the modes of vibration described in 3.2.3 or 3.2.9 whenthe imposed frequency is such that the resultant displacementsfor a given amount of driving force are at a maximum.3.2.7.1 DiscussionThe resonant frequencies are naturalvibration f
40、requencies that are determined by the modulus ofelasticity, 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-sectional dimension is at least five and preferably in the rangefrom 20 to 25.3.2.9 t
41、orsional vibrations, noscillations that occur in eachcross-sectional plane of a slender rod or bar, such that the planetwists around the length dimension axis.4. Summary of Test Method4.1 This test method measures the resonant frequencies oftest specimens of suitable geometry by exciting them atcont
42、inuously variable frequencies. Mechanical excitation ofthe bars is provided through 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
43、electrical signal. The amplitude and frequency of thesignal are measured by an oscilloscope 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 meth
44、od 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 stresses are applied to the specimen, thus minimizingthe possibility of fracture.5.1.2 The period of time during which measurement stressis
45、applied and removed is of the order of hundreds ofmicroseconds. With this test method it is feasible to performmeasurements at high temperatures, where delayed elastic andcreep effects would invalidate modulus of elasticity measure-ments calculated from static loading.5.2 This test method is suitabl
46、e for detecting whether amaterial meets the 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. S
47、pecimen 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 toconve
48、rt the 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-t
49、ion 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,microammeter, or oscilloscope. An oscilloscope is recom-mended because it enables the operator to positively identifyresonances, including higher order harmonics, by Lissajousfigure analysis. If a Lissajous figure is desired, the output of theoscillator is also coupled to the horizontal plates of theoscilloscope. If temperature-depend
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