Designation: C747 − 16 An American National StandardStandard Test Method forModuli of Elasticity and Fundamental Frequencies ofCarbon and Graphite Materials by Sonic Resonance1This standard is issued under the fixed designation C747; the number immediately following the designation indicates the year oforiginal adoption or, in the case 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. Scope*1.1 This test method covers determination of the dynamicelastic properties of isotropic and near isotropic carbon andgraphite materials at ambient temperatures. Specimens of thesematerials possess specific mechanical resonant frequencies thatare determined by the elastic modulus, mass, and geometry ofthe test specimen. The dynamic elastic properties of a materialcan therefore be computed if the geometry, mass, and mechani-cal resonant frequencies of a suitable (rectangular or cylindri-cal) test specimen of that material can be measured. DynamicYoung’s modulus is determined using the resonant frequencyin the flexural or longitudinal mode of vibration. The dynamicshear modulus, or modulus of rigidity, is found using torsionalresonant vibrations. Dynamic Young’s modulus and dynamicshear modulus are used to compute Poisson’s ratio.1.2 This test method determines elastic properties by mea-suring the fundamental resonant frequency of test specimens ofsuitable geometry by exciting them mechanically by a singularelastic strike with an impulse tool. Specimen supports, impulselocations, and signal pick-up points are selected to induce andmeasure specific modes of the transient vibrations. A trans-ducer (for example, contact accelerometer or non-contactingmicrophone) senses the resulting mechanical vibrations of thespecimen and transforms them into electric signals. (See Fig.1.) The transient signals are analyzed, and the fundamentalresonant frequency is isolated and measured by the signalanalyzer, which provides a numerical reading that is (or isproportional to) either the frequency or the period of thespecimen vibration. The appropriate fundamental resonantfrequencies, dimensions, and mass of the specimen are used tocalculate dynamic Young’s modulus, dynamic shear modulus,and Poisson’s ratio. AnnexA1 contains an alternative approachusing continuous excitation.1.3 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.4 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 safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2C215 Test Method for Fundamental Transverse,Longitudinal, and Torsional Resonant Frequencies ofConcrete SpecimensC559 Test Method for Bulk Density by Physical Measure-ments of Manufactured Carbon and Graphite ArticlesC885 Test Method for Young’s Modulus of RefractoryShapes by Sonic ResonanceC1161 Test Method for Flexural Strength of AdvancedCeramics at Ambient TemperatureE111 Test Method for Young’s Modulus, Tangent Modulus,and Chord ModulusE177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE228 Test Method for Linear Thermal Expansion of SolidMaterials With a Push-Rod DilatometerE691 Practice for Conducting an Interlaboratory Study toDetermine the Precision of a Test Method3. Terminology3.1 Definitions:3.1.1 antinodes, n—two 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.3.1.2 elastic modulus—the ratio of stress to strain, in thestress range where Hooke’s law is valid.3.1.3 flexural vibrations, n—the vibrations that occur whenthe displacements in a slender rod or bar are in a plane normalto the length dimension.1This test method is under the jurisdiction of ASTM Committee D02 onPetroleum Products, Liquid Fuels, and Lubricants and is the direct responsibility ofSubcommittee D02.F0 on Manufactured Carbon and Graphite Products.Current edition approved Oct. 1, 2016. Published January 2017. Originallyapproved in 1974. Last previous edition approved in 2010 as C747 – 93 (2010)ɛ1.DOI: 10.1520/C0747-16.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at

[email protected] For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.*A Summary of Changes section appears at the end of this standardCopyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United StatesThis international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.13.1.4 homogeneous, adj—in carbon and graphitetechnology, the condition of a specimen such that the compo-sition and density are uniform, so that any smaller specimentaken from the original is representative of the whole.Practically, as long as the geometrical dimensions of the testspecimen are large with respect to the size of individual grains,crystals, components, pores, or microcracks, the body can beconsidered homogeneous.3.1.5 in-plane flexure, n—for rectangular parallelepipedgeometries, a flexure mode in which the direction of displace-ment is in the major plane of the test specimen.3.1.6 isotropic, adj—in carbon and graphite technology,having an isotropy ration of 0.9 to 1.1 for a specific property ofinterest.3.1.7 longitudinal vibrations—when the oscillations in aslender rod or bar are in a plane parallel to the lengthdimension, the vibrations are said to be in the longitudinalmode.3.1.8 nodes, n—one or more locations in a slender rod or barin resonance having a constant zero displacement. For thefundamental flexural resonance of such a rod or bar, the nodesare located at 0.224 L from each end, where L is the length ofthe specimen.3.1.9 out-of-plane flexure, n—for rectangular parallelepipedgeometries, a flexure mode in which the direction of displace-ment is perpendicular to the major plane of the test specimen.3.1.10 Poisson’s ration (µ), n—the absolute value of theratio of transverse strain to the corresponding axial strainresulting from uniformly distributed axial stress below theproportional limit of the material. Young’s Modulus (E), shearmodulus (G), and Poisson’s ratio (µ) are related by thefollowing equation:µ 5 ~E ⁄2G! 2 1 (1)3.1.11 resonant frequency, n—naturally 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.3.1.12 shear modulus, n—the elastic modulus in shear ortorsion. Also called modulus of rigidity or torsional modulus.3.1.13 torsional vibrations, n—the vibrations that occurwhen the oscillations in each cross-sectional plane of a slenderrod or bar are such that the plane twists around the lengthdimension axis.3.1.14 transverse vibrations, n—when the oscillations in aslender rod or bar are in a horizontal plane normal to the lengthdimension, the vibrations are said to be in the transverse mode.This mode is also commonly referred to as the flexural modewhen the oscillations are in a vertical plane.3.1.15 Young’s modulus, n—the elastic modulus in tensionor compression.4. Summary of Test Method4.1 This test method measures the fundamental resonantfrequency of test specimens of suitable geometry (bar or rod)by exciting them mechanically by a singular elastic strike withan impulse tool. A transducer (for example, contact accelerom-eter or non-contacting microphone) senses the resulting me-chanical vibrations of the specimen and transforms them intoelectric signals. Specimen supports, impulse locations, andsignal pick-up points are selected to induce and measurespecific modes of the transient vibrations. The signals areanalyzed, and the fundamental resonant frequency is isolatedand measured by the signal analyzer, which provides a numeri-cal reading that is (or is proportional to) either the frequency orthe period of the specimen vibration. The appropriate funda-mental resonant frequencies, dimensions, and mass of thespecimen are used to calculate dynamic Young’s modulus,dynamic shear modulus, and Poisson’s ratio.5. Significance and Use5.1 This test method may be used for material development,characterization, design data generation, and quality controlpurposes.5.2 This test method is primarily concerned with the roomtemperature determination of the dynamic moduli of elasticityand rigidity of slender rods or bars composed of homoge-neously distributed carbon or graphite particles.5.3 This test method can be adapted for other materials thatare elastic in their initial stress-strain behavior, as defined inTest Method E111.5.4 This basic test method can be modified to determineelastic moduli behavior at temperatures from –75 °C to +2500°C. Thin graphite rods may be used to project the specimenextremities into ambient temperature conditions to provideresonant frequency detection by the use of transducers asdescribed in 7.1.FIG. 1 Block Diagram of Typical Test ApparatusC747 − 1626. 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 the moduli is applicableto inhomogeneous materials only with careful consideration ofthe effect of inhomogeneities and anisotropy. The character(volume fraction, size, morphology, distribution, orientation,elastic properties, and interfacial bonding) of inhomogeneitiesin the specimens will have a direct effect on the elasticproperties of the specimen as a whole. These effects must beconsidered in interpreting the test results for composites andinhomogeneous materials.6.1.2 The procedure involves measuring transient 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, etching, etc.) change the elastic properties of thenear-surface material, there may be accentuated effects on theproperties measured by this flexural method, as compared tostatic bulk measurements by tensile or compression testing.6.1.4 The test method is not satisfactory for specimens thathave 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 parallelepipedand cylinders) for which analytical equations are available torelate geometry, mass, and modulus to the resonant vibrationfrequencies. The test method is not appropriate for determiningthe elastic properties of materials that cannot be fabricated intosuch 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 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 onflexure bars prepared according to Test Method C1161 willchange the resonant frequency of the test bars and introduceerror into the calculations of the dynamic modulus. It isrecommended that specimens for this test method not havechamfered or rounded edges.6.2.3 For specimens with as-fabricated and rough or unevensurfaces, variations in dimensions 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 The test method assumes that the specimen is vibratingfreely, with no significant restraint or impediment. Specimensupports should be designed and located properly in accor-dance with 9.3.1, 9.4.1, and 9.5.1 so the specimen can vibratefreely in the desired mode. In using direct contact transducers,the transducer should be positioned away from antinodes andwith minimal force to avoid interference with free vibration.With non-contacting transducers, the maximum sensitivity isaccomplished by placing the transducer at an antinode.6.4 Proper location of the impulse point and transducer isimportant in introducing and measuring the desired vibrationmode. The locations of the impulse point and transducer shouldnot be changed in multiple readings; changes in position maydevelop and detect alternative vibration modes. In the samemanner, the force used in impacting should be consistent inmultiple readings.6.5 If the frequency readings are not repeatable for aspecific set of impulse and transducer locations on a specimen,it may be because several different modes of vibration arebeing developed and detected in the test. The geometry of thetest bar and desired vibration mode should be evaluated andused to identify the nodes and antinodes of the desiredvibrations. More consistent measurements may be obtained ifthe impulse point and transducer locations are shifted to induceand measure the single desired mode of vibration.7. Apparatus7.1 Apparatus suitable for accurately detecting, analyzing,and measuring the fundamental resonant frequency or period ofa vibrating free beam is used. The test apparatus is shown inFig. 1. It consists of an impulser, a suitable pickup transducerto convert the mechanical vibration into an electrical signal, anelectronic system (consisting of a signal conditioner/amplifier,a signal analyzer, and a frequency readout device), and asupport system. Commercial instrumentation is available thatmeasures the frequency or period of the vibrating specimen.7.2 Impulser—The exciting impulse is imparted by lightlystriking the specimen with a suitable implement. This imple-ment should have most of its mass concentrated at the point ofimpact and have mass sufficient to induce a measurablemechanical vibration, but not so large as to displace or damagethe specimen physically. In practice, the size and geometry ofthe impulser depends on the size and weightand elasticproperties of the specimen and the force needed to producevibration. For comm