1、Designation: C 747 93 (Reapproved 2005)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 C 747; the number immediately following the designation
2、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 (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method covers the measureme
3、nt of the funda-mental transverse, longitudinal, and torsional frequencies ofisotropic and anisotropic carbon and graphite materials. Thesemeasured resonant frequencies are used to calculate dynamicelastic moduli for any grain orientations.1.2 The values stated in SI units are to be regarded as thes
4、tandard.1.3 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. Refe
5、renced Documents2.1 ASTM Standards:2C 215 Test Method for Fundamental Transverse, Longitu-dinal, and Torsional Frequencies of Concrete SpecimensC 559 Test Method for Bulk Density by Physical Measure-ment of Manufactured Carbon and Graphite ArticlesC 885 Test Method for Youngs Modulus of RefractorySh
6、apes by Sonic ResonanceE 111 Test Method forYoungs Modulus, Tangent Modulus,and Chord Modulus3. Terminology3.1 Definitions of Terms Specific to This Standard:3.1.1 elastic modulusthe initial tangent modulus as de-fined in Test Method E 111.3.1.2 longitudinal vibrationswhen the oscillations in aslend
7、er rod or bar are in a plane parallel to the lengthdimension, the vibrations are said to be in the longitudinalmode (Fig. 1(a).3.1.3 nodal pointsa slender rod or bar in resonancecontains one or more points having zero displacement, callednodal points. In the longitudinal and torsional fundamentalres
8、onances of a uniform rod or bar, the mid-length point is thenodal point (Fig. 1(a) and Fig. 1(d). For the fundamentaltransverse or flexural resonance, the nodal points are located at0.224 L from each end, where L is the length of the specimen(Fig. 1(b) and Fig. 1(c).3.1.4 resonancea slender rod or b
9、ar driven into one of theabove modes of vibration is said to be in resonance when theimposed frequency is such that resultant displacements for agiven amount of driving force (voltage) are at a maximum. Theresonant frequency is a natural vibration frequency which isdetermined by the elastic moduli,
10、density, and dimensions ofthe test specimen.1This test method is under the jurisdiction of ASTM Committee D02 onPetroleum Products and Lubricants and is the direct responsibility of SubcommitteeD02.F0 on Manufactured Carbon and Graphite Products.Current edition approved May 1, 2005. Published May 20
11、05. Originallyapproved in 1974. Last previous revision approved in 1998 as C 747 93 (1998).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 Su
12、mmary page onthe ASTM website.FIG. 1 Resonance Modes1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.1.5 slender rod or bara specimen whose ratio of lengthto minimum cross-sectional dimension is at least 5 but notmore than 20.3.1.6
13、transverse vibrationswhen the oscillations in a slen-der rod or bar are in a horizontal plane normal to the lengthdimension, the vibrations are said to be in the transverse mode(Fig. 1(b). This mode is also commonly referred to as theflexural mode when the oscillations are in a vertical plane (Fig.1
14、(c). Either the transverse or flexural mode of specimenvibration will yield the correct fundamental frequency, subjectto the geometric considerations given in 9.1.3.1.7 torsional vibrationswhen the oscillations in eachcross-sectional plane of a slender rod or bar are such that theplane twists around
15、 the length dimension axis, the vibrationsare said to be in the torsional mode (Fig. 1(d).4. Summary of Test Method4.1 The dynamic methods of determining the elastic moduliare based on the measurement of the fundamental resonantfrequencies of a slender rod of circular or rectangular crosssection. Th
16、e resonant frequencies are related to the specimendimensions and material properties as follows:4.1.1 Transverse or Flexural ModeThe equation for thefundamental resonant frequency of the transverse or flexuralmode of vibration is as follows:E 5 CMf2(1)where:E = elastic modulus, Pa,C = a dimensional
17、constant that depends upon the shapeand size of the specimen, and Poissons ratio. Theunits of C are to be consistent with those of E, M, andf,M = mass of the specimen, kg, andf = frequency of fundamental transverse or flexural modeof vibration, Hz.4.1.2 Longitudinal ModeThe equation for the fundamen
18、-tal resonant frequency of the longitudinal mode of variation isas follows:E 5 Df2L2r (2)where:E = elastic modulus, Pa,D = a constant consistent with the units of E, f, and L,f = frequency of fundamental longitudinal mode of vibra-tion, Hz,L = length of the specimen, m, andr = density of the specime
19、n as determined by Test MethodC 559, kg/m3.4.1.3 Torsional ModeThe equation for the fundamentalresonant frequency of the torsional mode of vibration is asfollows:G 5 RBf2L2r (3)where:G = modulus of rigidity, Pa,R = ratio of the polar moment of inertia to the shape factorfor torsional rigidity,B = a
20、constant consistent with the units of G, R, f, L, and r,f = frequency of fundamental torsional mode of vibration,Hz,L = length of the specimen, m, andr = density of the specimen as determined by Test MethodC 559, kg/m3.5. Significance and Use5.1 This test method is primarily concerned with the roomt
21、emperature determination of the dynamic moduli of elasticityand rigidity of slender rods or bars composed of homoge-neously distributed carbon or graphite particles.5.2 This test method can be adapted for other materials thatare elastic in their initial stress-strain behavior, as defined inTest Meth
22、od E 111.5.3 This basic test method can be modified to determineelastic moduli behavior at temperatures from 75C to+2500C. Thin graphite rods may be used to project thespecimen extremities into ambient temperature conditions toprovide resonant frequency detection by the use of transducersas describe
23、d in 6.1.6. Apparatus6.1 The fundamental resonant frequencies for the differentmodes of vibration of a test specimen can be determined byseveral established testing procedures. The apparatus describedherein uses phonograph record pickup cartridges as a conve-nient method of generating and detecting
24、these frequencies. Atypical testing apparatus is shown schematically in Fig. 2.6.1.1 Driving CircuitThe driving circuit consists of avariable-frequency oscillator and a record pickup cartridgeassembly. It is recommended that a variable-frequency oscil-lator be used in conjunction with a digital-freq
25、uency counter.FIG. 2 Schematic Diagram of Typical Dynamic Elastic ModulusDetection ApparatusC 747 93 (2005)2The oscillator shall have sufficient power output to inducedetectable vibrations in the test specimen at frequencies aboveand below the fundamental frequency under consideration.Means for cont
26、rolling the output of the oscillator shall beprovided. The vibrating needle of the driving unit shall besmall in mass as compared to the test specimen, and a meansshall be provided to maintain a minimal contact pressure on thespecimen. Either a piezoelectric or magnetic driving unitmeeting these req
27、uirements may be used.6.1.2 Pickup CircuitThe pickup circuit consists of arecord pickup cartridge, amplifier, optional high-pass filter, andan indicating meter or cathode-ray oscilloscope. The pickupunit shall generate a voltage proportional to the amplitude,velocity, or acceleration of the test spe
28、cimen. Either a piezo-electric or magnetic pickup unit meeting these conditions maybe used. The amplifier shall have a controllable output ofsufficient magnitude to sharply peak out the resonant frequen-cies on the indicating meter or the cathode-ray oscilloscopedisplay tube. It may be necessary to
29、use a high-pass filter inorder to reduce room noise and spurious vibrations. Theindicating meter may be a voltmeter, microammeter or oscil-loscope. An oscilloscope is recommended because it enablesthe operator to positively identify resonances, including higherorder harmonics, by Lissajous figure an
30、alysis.6.1.3 Specimen SupportsThe supports shall permit thespecimen to oscillate without significant restriction in thedesired mode. This is accomplished for all modes by support-ing the specimen at its transverse fundamental nodal points(0.224 L from each end). The supports should have minimalarea
31、in contact with the specimen and shall be of cork, rubber,or similar material. In order to properly identify resonantfrequencies, the receiver record pickup cartridge must bemovable along the total specimen length. Provisions shall bemade to adjust contact pressures of both record pickup car-tridges
32、 in order to accommodate specimen size variations. Theentire specimen support structure shall be mounted on amassive base plate resting on vibration isolators.7. Test Specimens7.1 Selection and Preparation of SpecimensIn the selec-tion and preparation of test specimens, take special care toobtain re
33、presentative specimens that are straight, uniform incross section, and free of extraneous liquids.7.2 Measurement of Weight and DimensionsDeterminethe weight and the average length of the specimens within60.5 %. Determine average specimen cross-sectional dimen-sion within 61%.7.3 Limitations on Dime
34、nsional Ratio Specimens havingeither very small or very large ratios of length to thickness maybe difficult to excite in the fundamental modes of vibration. Forthis method, the ratio must be between 5 and 20 (slender rodlimitations).8. Procedure8.1 Switch on all electrical equipment and allow to sta
35、bilizein accordance with the manufacturers recommendations. (Useof a metal bar as a calibration standard is recommended tocheck equipment response and accuracy. Dimensional mea-surements and weight shall meet the requirements of 7.2.)8.2 Transverse Fundamental Resonance Frequency:8.2.1 Place the spe
36、cimen on the supports, which are locatedat the fundamental transverse nodal points (0.224 L from eachend). Place the driving and pickup-unit vibrating needles on thespecimen center line at its extreme opposite ends with aminimal contact pressure consistent with good response. Thevibrating direction
37、of the driving and pickup needles must beperpendicular to the length of the specimen (Fig. 1(b).8.2.2 Force the test specimen to vibrate at various frequen-cies and simultaneously observe the amplified output on anindicating meter or oscilloscope. Record the frequency ofvibration of the specimen tha
38、t results in a maximum displace-ment, having a well-defined peak on the indicator, where nodalpoint tracking indicates fundamental transverse resonance.8.2.3 A basic understanding of Lissajous patterns as dis-played on an oscilloscope cathode ray tube (CRT), will aid inthe proper identification of t
39、he modes of vibration and har-monic frequencies observed. As the oscillator frequency levelis increased from a point well below expected resonance, asingle closed loop Lissajous pattern tilted from the horizontalreference plane, will eventually be displayed on the CRT. Thispattern denotes a resonanc
40、e mode. The nodal points dynamicmodulus tracking guide template (Fig. 3) may be used toidentify any resonant mode.8.2.4 Move the pickup cartridge needle slowly toward thespecimen center and observe the Lissajous pattern loop.Fundamental transverse resonance is indicated when the fol-lowing condition
41、s prevail:8.2.4.1 The loop pattern flattens to a horizontal line with thepickup needle over the specimen support.8.2.4.2 The CRT pattern opens up to a full loop in adirection normal to its original direction, with the pickupneedle over the specimen center.8.2.5 Return the pickup needle to its origin
42、al position at thespecimen end.8.2.6 Spurious resonating frequency modes may mask orattenuate the fundamental transverse frequency indication.Investigation of higher order harmonic resonating frequenciesby use of the tracking guide template (Fig. 3) will help toidentify the correct fundamental frequ
43、ency mode. A plot of theratio of harmonic to fundamental frequency for transversemode of vibration (Fig. 4) may then be used to calculate thefundamental transverse resonant frequency mode.8.3 Longitudinal Fundamental Resonance Frequency:8.3.1 Leave the specimen supported at the fundamentaltransverse
44、 mode nodal points as in 8.2.1. Rotate the drivingunit and pickup cartridge needles so as to induce vibrationsparallel to the specimen length (Fig. 1(a).8.3.2 Force the test specimen to vibrate as in 8.2.2. Recordthe frequency of vibration of the test specimen, where nodalpoint tracking indicates fu
45、ndamental longitudinal resonance.The second harmonic longitudinal resonant frequency is twicethe fundamental longitudinal resonant frequency.8.4 Torsional Fundamental Resonance Frequency:8.4.1 Leave the specimen supported as in 8.2.1. Rotate thedriving unit and pickup cartridge needles so as to indu
46、cevibrations perpendicular to the length of the sample (Fig. 1(d).C 747 93 (2005)38.4.2 Force the specimen to vibrate as in 8.2.2. Record thefrequency of vibration of the test specimen, where nodal pointtracking indicates fundamental torsional resonance. The sec-ond harmonic torsional resonant frequ
47、ency is twice the funda-mental torsional resonant frequency.9. Calculation9.1 Calculate the dynamic modulus of elasticity for thetransverse or flexural mode of vibration from the fundamentaltransverse frequency, weight, and dimensions of the testspecimen as follows:Dynamic E 5 CMf2(4)where units are
48、 as defined in 3.1.1. The evaluation of theconstant C, because of the complexity of its determination, isin tabular form. Eq 4 may be rewritten in the forms:Dynamic E pascals!5AcMf2/d for rods withcircular cross sections (5)where d is the diameter of the rod in metres, andDynamic E pascals!5ARMf2/w
49、for bars withsquare or rectangular cross sections (6)where w is the width dimension of the bar in metres.9.1.1 Values of Acand ARare shown in Annex A1 underTable A1.1 and Table A1.2. The value of Acis given as afunction of the diameter-to-length ratio of the sample. Thevalue of ARis given as a function of the ratio of the dimensionin the direction of vibration, t, to the length. The dimension, w,is perpendicular to the vibration direction, as shown in Fig. 5.Table A1.1 and Table A1.2 have been calculated for threevalues of Poissons ratio (). The
