1、Designation: E 1876 09Standard 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 () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method covers determination of the dynamicelastic properties of elastic materials
3、 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 reson
4、ant 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 using
5、 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 appropriatemodificatio
6、ns 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 andcalc
8、ulations are consistent with these test methods.1.4 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.5 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibilit
9、y 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. Referenced Documents2.1 ASTM Standards:2C 215 Test Method for Fundamental Transverse, Longitu-dinal, and Torsional Resonant Frequencies of C
10、oncreteSpecimensC 372 Test Method for Linear Thermal Expansion 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 Modu
11、li of Elasticity and Fundamen-tal Frequencies of Carbon 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 Me
12、thod 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 Excitation of VibrationE6 Terminology Relating to Methods of Mechanical Test-ingE 1
13、77 Practice for Use of the Terms Precision and Bias inASTM Test Methods1This 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 April 1, 2009. Published April 2009. Origi
14、nallyapproved in 1997. Last previous edition approved in 2007 as E 1876 07.2For 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
15、 ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3. 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 thi
16、s test method.3.1.1 dynamic mechanical measurement, 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 str
17、ess that amaterial is capable of sustaining without 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 corres
18、ponding 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 equation: 5 E/2G! 1 (1)E63.1.5 proportional limit FL2
19、, nthe greatest stress that amaterial is capable of 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 ela
20、stic modulus intension or compression. E63.2 Definitions 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 loca
21、ted at the two ends and thecenter 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, which will be eliminated uponremoval of the
22、stress, with the body returning instantly to itsoriginal 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
23、 normal tothe length dimension.3.2.4 homogeneous, adjthe 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
24、respect to the size of individualgrains, crystals, 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 isotr
25、opic, 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 a mac-roscopic scale, if they are homogeneous and there is a randomdistribution and orientation of phases, crystallites, components,
26、pores, or microcracks.3.2.7 longitudinal vibrations, 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 fundame
27、ntal flexural resonance of such a rod or bar, thenodes 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 t
28、est specimen.3.2.10 resonant frequency, nnaturally 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 reson
29、ant frequencyof that mode.3.2.11 slender rod or bar, 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
30、cross-sectional plane of a slenderrod or bar are such 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 a
31、n impulsetool. A transducer (for example, contact accelerometer 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 specificm
32、odes of the transient vibrations. The signals are analyzed, 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
33、 resonantfrequencies, dimensions, and mass of the specimen 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.E187
34、60925.2 This test method is specifically appropriate 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 (cyli
35、ndrical). Flat platesand disks may also be measured 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
36、.4.1 The test method is nondestructive in nature and 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 t
37、est uses an impact tool andsimple supports for the 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 b
38、oth regular and complex shapes. A range ofacceptable 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 suit
39、able for testing by other procedures. Any specimenwith 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 sp
40、ecimen must possess if its geometry andmass are within 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
41、 so forth. Speci-men descriptions should include any 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, isot
42、ropic materials.6.1.1 This method of determining the 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 interfa
43、cial bonding) of thereinforcement and inhomogeneities 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 tran
44、sient elasticvibrations. Materials with very high damping 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, et
45、ching, and so forth) change the elastic properties 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 thath
46、ave major discontinuities, such as large cracks (internal 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 modul
47、us to the resonantvibration frequencies. This test 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.Deviation
48、s from the specified tolerances for the dimensions 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 bar
49、s and introduce error intothe calculations of the dynamic 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 meth
