1、Designation: E 1876 07Standard Test Method forDynamic Youngs Modulus, Shear Modulus, and PoissonsRatio by Impulse Excitation of Vibration1This standard is issued under the fixed designation E 1876; the number immediately following the designation indicates the year oforiginal adoption or, in the cas
2、e 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 determination of the dynamicelastic properties of elastic material
3、s at ambient temperatures.Specimens of these materials possess specific mechanicalresonant frequencies that are determined by the elastic modu-lus, mass, and geometry of the test specimen. The dynamicelastic properties of a material can therefore be computed if thegeometry, mass, and mechanical reso
4、nant frequencies of asuitable (rectangular or cylindrical geometry) test specimen ofthat material can be measured. Dynamic Youngs modulus isdetermined using the resonant frequency in either the flexuralor longitudinal mode of vibration. The dynamic shear modulus,or modulus of rigidity, is found usin
5、g torsional resonantvibrations. Dynamic Youngs modulus and dynamic shearmodulus are used to compute Poissons ratio.1.2 Although not specifically described herein, this testmethod can also be performed at cryogenic and high tempera-tures with suitable equipment modifications and appropriatemodificati
6、ons to the calculations to compensate for thermalexpansion.1.3 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
7、, 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 andcal
8、culations are consistent with these test methods.1.4 The values stated in SI units are to be regarded as thestandard.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-priat
9、e safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2C 215 Test Method for Fundamental Transverse, Longitu-dinal, and Torsional Resonant Frequencies of ConcreteSpecimensC 372 Test Method for Linear Thermal Ex
10、pansion of Por-celain Enamel and Glaze Frits and Fired Ceramic Whitew-are Products by the Dilatometer MethodC 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
11、 and Graphite Materials by SonicResonanceC 848 Test Method for Youngs Modulus, Shear Modulus,and Poissons Ratio For Ceramic Whitewares by Reso-nanceC 1161 Test Method for Flexural Strength of AdvancedCeramics at Ambient TemperatureC 1198 Test Method for Dynamic Youngs Modulus, ShearModulus, and Pois
12、sons Ratio for Advanced Ceramics bySonic ResonanceC 1259 Test Method for Dynamic Youngs Modulus, ShearModulus, and Poissons Ratio for Advanced Ceramics byImpulse Excitation of VibrationE6 Terminology Relating to Methods of Mechanical Test-ing1This test method is under the jurisdiction of ASTM Commit
13、tee E28 onMechanical Testing and is the direct responsibility of Subcommittee E28.04 onUniaxial Testing.Current edition approved June 1, 2007. Published June 2007. Originallyapproved in 1997. Last previous edition approved in 2006 as E 1876 01(2006).2For referenced ASTM standards, visit the ASTM web
14、site, 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.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United Sta
15、tes.E 177 Practice for Use of the Terms Precision and Bias inASTM Test Methods3. Terminology3.1 DefinitionsThe definitions of terms relating to me-chanical testing appearing in Terminology E 6 should beconsidered as applying to the terms used in this test method.3.1.1 dynamic mechanical measurement,
16、 na 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 combinationthereof.3.1.2 elastic limit FL2, nthe greatest stress that amaterial is capable of sustaining without
17、 permanent strainremaining upon complete release of the stress. E63.1.3 elastic modulus FL2, nthe ratio of stress to strainbelow the proportional limit. E63.1.4 Poissons ratio () nd, nthe absolute value of theratio of transverse strain to the corresponding axial strainresulting from uniformly distri
18、buted 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)E63.1.5 proportional limit FL2, nthe greatest stress that amaterial is capable of
19、 sustaining without deviation fromproportionality of stress to strain (Hookes law). E63.1.6 shear modulus (G) FL2, nthe elastic modulus inshear or torsion. Also called modulus of rigidity or torsionalmodulus. E63.1.7 Youngs modulus (E) FL2, nthe elastic modulus intension or compression. E63.2 Defini
20、tions of Terms Specific to This Standard:3.2.1 antinodes, ntwo or more locations that have localmaximum displacements, called antinodes, in an unconstrainedslender rod or bar in resonance. For the fundamental flexureresonance, the antinodes are located at the two ends and thecenter of the specimen.3
21、.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, which will be eliminated uponremoval of the stress, with the body returning instantly to itsori
22、ginal size and shape without energy loss. Most elasticmaterials conform to this definition well enough to make thisresonance test valid.3.2.3 flexural vibrations, nthe vibrations that occur whenthe oscillations in a slender rod or bar are in a plane normal tothe length dimension.3.2.4 homogeneous, a
23、djthe condition of a specimen suchthat the composition and density are uniform, so that anysmaller specimen taken from the original is representative ofthe whole. Practically, as long as the geometrical dimensions ofthe test specimen are large with respect to the size of individualgrains, crystals,
24、components, pores, or microcracks, the bodycan be considered homogeneous.3.2.5 in-plane flexure, nfor rectangular parallelepipedgeometries, a flexure mode in which the direction of displace-ment is in the major plane of the test specimen.3.2.6 isotropic, adjthe condition of a specimen such thatthe v
25、alues of the elastic properties 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, components,pores, or microcracks.3.2.7 longitudinal vibrations
26、, nthe vibrations that occurwhen the oscillations in a slender rod or bar are parallel to thelength of the rod or bar.3.2.8 nodes, na slender rod or bar in resonance containingone or more locations having a constant zero displacement. Forthe fundamental flexural resonance of such a rod or bar, theno
27、des are located at 0.224 L from each end, where L is thelength of the specimen.3.2.9 out-of-plane flexure, nfor rectangular parallelepipedgeometries, a flexure mode in which the direction of displace-ment is perpendicular to the major plane of the test specimen.3.2.10 resonant frequency, nnaturally
28、occurring frequen-cies of a body driven into flexural, torsional, or longitudinalvibration that are determined by the elastic modulus, mass, anddimensions of the body. The lowest resonant frequency in agiven vibrational mode is the fundamental resonant frequencyof that mode.3.2.11 slender rod or bar
29、, nin dynamic elastic propertytesting, a specimen whose ratio of length to minimum cross-sectional dimension is at least 5 and preferably in the rangefrom 20 to 25.3.2.12 torsional vibrations, nthe vibrations that occurwhen the oscillations in each cross-sectional plane of a slenderrod or bar are su
30、ch that the plane twists around the lengthdimension axis.4. Summary of Test Method4.1 This test method measures the fundamental resonantfrequency of test specimens of suitable geometry by excitingthem mechanically by a singular elastic strike with an impulsetool. A transducer (for example, contact a
31、ccelerometer ornon-contacting microphone) senses the resulting mechanicalvibrations of the specimen and transforms them into electricsignals. Specimen supports, impulse locations, and signalpick-up points are selected to induce and measure specificmodes of the transient vibrations. The signals are a
32、nalyzed, andthe fundamental resonant frequency is isolated and measuredby the signal analyzer, which provides a numerical reading thatis (or is proportional to) either the frequency or the period ofthe specimen vibration. The appropriate fundamental resonantfrequencies, dimensions, and mass of the s
33、pecimen are used tocalculate dynamic Youngs modulus, dynamic shear modulus,and Poissons ratio.5. Significance and Use5.1 This test method may be used for material development,characterization, design data generation, and quality controlpurposes.E18760725.2 This test method is specifically appropriat
34、e for deter-mining the modulus of materials that are elastic, homogeneous,and isotropic (1).35.3 This test method addresses the room temperature deter-mination of dynamic moduli of elasticity of slender bars(rectangular cross section) and rods (cylindrical). Flat platesand disks may also be measured
35、 similarly, but the requiredequations for determining the moduli are not addressed herein.5.4 This dynamic test method has several advantages anddifferences from static loading techniques and from resonanttechniques requiring continuous excitation.5.4.1 The test method is nondestructive in nature an
36、d can beused for specimens prepared for other tests. The specimens aresubjected to minute strains; hence, the moduli are measured ator near the origin of the stress-strain curve, with the minimumpossibility of fracture.5.4.2 The impulse excitation test uses an impact tool andsimple supports for the
37、test specimen. There is no requirementfor complex support systems that require elaborate setup oralignment.5.5 This technique can be used to measure resonant frequen-cies alone for the purposes of quality control and acceptance oftest specimens of both regular and complex shapes. A range ofacceptabl
38、e resonant frequencies is determined for a specimenwith a particular geometry and mass. The technique is particu-larly suitable for testing specimens with complex geometries(other than parallelepipeds, cylinders/rods, or disks) that wouldnot be suitable for testing by other procedures. Any specimenw
39、ith a frequency response falling outside the prescribedfrequency 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 wit
40、hin specified tolerances.5.6 If a thermal treatment or an environmental exposureaffects the elastic response of the test specimen, this testmethod may be suitable for the determination of specific effectsof thermal history, environment exposure, and so forth. Speci-men descriptions should include an
41、y specific thermal treat-ments or environmental exposures that the specimens havereceived.6. Interferences6.1 The relationships between resonant frequency and dy-namic modulus presented herein are specifically applicable tohomogeneous, elastic, isotropic materials.6.1.1 This method of determining th
42、e moduli is applicableto composite and inhomogeneous materials only with carefulconsideration of the effect of inhomogeneities and anisotropy.The character (volume fraction, size, morphology, distribution,orientation, elastic properties, and interfacial bonding) of thereinforcement and inhomogeneiti
43、es in the specimens will havea direct effect on the elastic properties of the specimen as awhole. These effects must be considered in interpreting the testresults for composites and inhomogeneous materials.6.1.2 The procedure involves measuring transient elasticvibrations. Materials with very high d
44、amping capacity may bedifficult to measure with this technique if the vibration dampsout before the frequency counter can measure the signal(commonly within three to five cycles).6.1.3 If specific surface treatments (coatings, machining,grinding, etching, and so forth) change the elastic properties
45、ofthe near-surface material, there will be accentuated effects onthe properties measured by this flexural method, as comparedto static/bulk measurements by tensile or compression testing.6.1.4 This test method is not satisfactory for specimens thathave major discontinuities, such as large cracks (in
46、ternal orsurface) or voids.6.2 This test method for determining moduli is limited tospecimens with regular geometries (rectangular parallelepiped,cylinders, and disks) for which analytical equations are avail-able to relate geometry, mass, and modulus to the resonantvibration frequencies. This test
47、method is not appropriate fordetermining the elastic properties of materials that cannot befabricated into such geometries.6.2.1 The analytical equations assume parallel and concen-tric dimensions for the regular geometries of the specimen.Deviations from the specified tolerances for the dimensions
48、ofthe specimens will change the resonant frequencies and intro-duce error into the calculations.6.2.2 Edge treatments such as chamfers or radii are notconsidered in the analytical equations. Edge chamfers changethe resonant frequency of the test bars and introduce error intothe calculations of the d
49、ynamic modulus. It is recommendedthat specimens for this test method not have chamfered orrounded edges.6.2.3 For specimens with as-fabricated and rough or unevensurfaces, variations in dimension can have a significant effectin the calculations. For example, in the calculation of dynamicmodulus, the modulus value is inversely proportional to thecube of the thickness. Uniform specimen dimensions andprecise measurements are essential for accurate results.6.3 This test method assumes that the specimen is vibratingfreely, wit
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