Designation: C769 − 15 An American National StandardStandard Test Method forSonic Velocity in Manufactured Carbon and GraphiteMaterials for Use in Obtaining an Approximate Value ofYoung’s Modulus1This standard is issued under the fixed designation C769; 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 a procedure for measuring thesonic velocity in manufactured carbon and graphite which canbe used to obtain an approximate value of Young’s modulus.1.2 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.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. Referenced Documents2.1 ASTM Standards:2C559 Test Method for Bulk Density by Physical Measure-ments of Manufactured Carbon and Graphite ArticlesC747 Test Method for Moduli of Elasticity and FundamentalFrequencies of Carbon and Graphite Materials by SonicResonanceIEEE/ASTM SI 10 Standard for Use of the InternationalSystem of Units (SI) (the Modern Metric System)3. Terminology3.1 Definitions:3.1.1 elastic modulus, n—the ratio of stress to strain, in thestress range where Hooke’s law is valid.3.1.2 Young’s modulus or modulus of elasticity (E), n—theelastic modulus in tension or compression.3.2 Definitions of Terms Specific to This Standard:3.2.1 end correction time (Te)—the non-zero time of flight(correction factor), measured in seconds, that may arise byextrapolation of the pulse travel time, corrected for zero time,back to zero sample length.3.2.2 longitudinal sonic pulse—a sonic pulse in which thedisplacements are in the direction of propagation of the pulse.3.2.3 pulse travel time, (Tt)—the total time, measured inseconds, required for the sonic pulse to traverse the specimenbeing tested, and for the associated electronic signals totraverse the transducer coupling medium and electronic circuitsof the pulse-propagation system.3.2.4 zero time, (T0)—the travel time (correction factor),measured in seconds, associated with the transducer couplingmedium and electronic circuits in the pulse-propagation sys-tem.4. Summary of Test Method4.1 The velocity of longitudinal sound waves passingthrough the test specimen is determined by measuring thedistance through the specimen and dividing by the time lapse,between the transmitted pulse and the received pulse.3,4Pro-vided the wavelength of the transmitted pulse is a sufficientlysmall fraction of the sample lateral dimensions, a value ofYoung’s modulus for isotropic graphite can then be obtainedusing Eq 1 and Eq 2:E 5 CvρV2(1)where:E = Young’s modulus of elasticity, Pa,ρ = density, kg/m3,V = longitudinal signal velocity, m/s, andCv= Poisson’s factor.The Poisson’s factor, Cν, is related to Poisson’s ratio, ν,bythe equation:Cν5~11ν!~1 2 2ν!1 2 ν(2)1This test method is under the jurisdiction of ASTM Committee D02 onPetroleum Products, Liquid Fuels, and Lubricantsand is the direct responsibility ofSubcommittee D02.F0 on Manufactured Carbon and Graphite Products.Current edition approved Dec. 1, 2015. Published January 2016. Originallyapproved in 1980. Last previous edition approved in 2009 as C769 – 09. DOI:10.1520/C0769-15.2For 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.3Schreiber, Anderson, and Soga, Elastic Constants and Their Measurement,McGraw-Hill Book Co., 1221Avenue of theAmericas, New York, NY 10020, 1973.4American Institute of Physics Handbook , 3rd ed., McGraw-Hill Book Co.,1221 Avenue of the Americas, New York, NY 10020, 1972, pp. 3–98ff.*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 States1If Poisson’s ratio is unknown, it can be assumed as anapproximation in the method. For nuclear graphites, a typicalPoisson’s ratio of 0.2 corresponds to a Poisson’s factor of 0.9.If the wavelength is not a small fraction of the sample lateraldimensions, and instead is much larger than the specimenlateral dimensions, then the Young’s modulus, E is given by Eq1 with Cνset to one rather than being determined by Eq 2.5. Significance and Use5.1 Sonic velocity measurements are useful for comparingmaterials with similar elastic properties, dimensions, andmicrostructure.5.2 Eq 1 provides an accurate value of Young’s modulusonly for isotropic, non-attenuative, and non-dispersive materi-als of infinite dimensions. For non-isotropic graphite, Eq 1 canbe modified to take into account the Poisson’s ratios in alldirections. As graphite is a strongly attenuative material, thevalue of Young’s modulus obtained with Eq 1 will be depen-dent on specimen length. If the specimen lateral dimensions arenot large compared to the wavelength of the propagated pulse,then the value of Young’s modulus obtained with Eq 1 will bedependent on the specimen lateral dimensions. The accuracy ofthe Young’s modulus calculated from Eq 1 will also dependupon the uncertainty in Poisson’s ratio and its impact on theevaluation of the Poisson’s factor in Eq 2. However, a value forYoung’s modulus can be obtained for many applications,which is often in good agreement with the value obtained byother more accurate methods, such as in Test Method C747.The technical issues and typical values of correspondinguncertainties are discussed in detail in STP 1578.55.3 If the grain size of the carbon or graphite is greater thanor about equal to the wavelength of the sonic pulse, the methodmay not be providing a value of Young’s modulus representa-tive of the bulk material. Therefore, it would be recommendedto test a lower frequency (longer wavelength) to demonstratethat the range of obtained velocity values are within anacceptable level of accuracy. Significant signal attenuationshould be expected when the grain size of the material isgreater than or about equal to the wavelength of the transmittedsonic pulse or the material is more porous than would beexpected for an as-manufactured graphite.NOTE 1—Due to frequency dependent attenuation in graphite, thewavelength of the sonic pulse through the test specimen is not necessarilythe same as the wavelength of the transmitting transducer.5.4 If the sample is only a few grains thick, the acceptabilityof the method’s application should be demonstrated by initiallyperforming measurements on a series of tests covering a rangeof sample lengths between the proposed test length and a testlength incorporating sufficient grains to adequately representthe bulk material.6. Apparatus6.1 Driving Circuit, consisting of an ultrasonic pulse gen-erator.6.1.1 The user should select a pulse frequency to suit thematerial microstructure and specimen elastic properties anddimensions being tested. High frequencies are attenuated bycarbon and graphite materials and, while typical practicablefrequencies lie in the range 0.5 MHz to 2.6 MHz, the user mayshow that frequencies outside this range are acceptable.6.2 Transducer, input, with suitable coupling medium (see8.5).6.3 Transducer, output, with suitable coupling medium (see8.5).6.3.1 The signal output will depend upon the characteristicsof the chosen transducers and pulser-receiver and the testmaterial. It is recommended that the user analyses the input andoutput frequency spectra to determine optimum conditions.Band pass filters and narrow band transducers may be used tosimplify the signal output which could improve the measure-ment of the time of flight.6.4 Computer, with analogue to digital converter, oroscilloscope, and external trigger from driving circuit.6.5 See Fig. 1 for a typical schematic setup.NOTE 2—Some manufacturers combine items 6.1 and 6.4 into a singlepackage with direct time readout. Such apparatus can operatesatisfactorily, provided the frequency of the propagated pulse is alreadyknown, in order to check that wavelength requirements for the method aresatisfied.7. Test Specimen7.1 Selection and Preparation of Specimens—Take specialcare to assure obtaining representative specimens that arestraight, uniform in cross section, and free of extraneousliquids. The specimen end faces shall be perpendicular to thespecimen cylindrical surface to within 0.125 mm total indicatorreading.7.2 Measurement of Weight and Dimensions—Determinethe weight and the average specimen dimensions to within60.2 %.7.3 Limitations on Dimensions—These cannot be preciselyspecified as they will depend upon the properties of thematerial being tested and the experimental setup (for example,transducer frequency). In order to satisfy the theory thatsupports Eq 1, as a guide, the specimen should have a diameterthat is at least a factor five, greater than the wavelength ofsound in the material under test. In practice, the length of thespecimen will be determined taking account of the commentsin 5.3 and 5.4.7.4 Limitations on Ultrasonic Pulse Frequency—Generallyspeaking, a better accuracy of time of flight will be obtained athigher frequencies. However, attenuation increases at higherfrequencies leading to weak and distorted signals.8. Procedure8.1 For any given apparatus and choice of couplingmedium, it is necessary to follow procedures to quantify thezero time, T0, and end correction time, Te, correction factors. T0will be dependent upon the type of transducers and theirperformance over time and should be regularly checked (see5ASTM Selected Technical Papers, STP 1578, Graphite Testing for NuclearApplications: The Significance of Test Specimen Volume and Geometry and theStatistical Significance of Test Specimen Population, 2014, edited by Tzelepi andCarroll.C769 − 1528.8). It must be quantified if the test setup is changed. Teshouldbe small and reflects the interaction between the couplingmedium and the test material. Teshould be determined once fora specific measurement setup and test material.8.1.1 Determine whether an end correction time, Te,isevident in the time of flight by performing time of flightmeasurements on various length samples taken from a singlebar. As modulus is likely to vary from sample to sample therecommended approach is to continually bisect a long rod,measuring each bi-section, until the required lower limit isreached. The end correction time, Te, is obtained from aregression fit to a graph of time of flight versus sample length.8.2 Measure and weigh the test specimen as in 7.2.8.3 Calculate the density of the test specimen in accordancewith Test Method C559.8.4 Connect the apparatus as shown in Fig. 1, and refer toequipment manufacturer’s instructions for setup precautions.Allow adequate time for equipment warm-up and stabilization.8.5 Place the transducers against the test specimen endfaces.8.5.1 A coupling medium may be necessary to improvetransmission of the sonic pulse. In this case, apply a lightcoating of the coupling medium to the faces of the testspecimens that will contact the transducers. Alternatively,rubber-tipped transducers can be effective if a fully noninva-sive measurement is needed.NOTE 3—The following coupling media may be used: hydroxyethylcellulose, petroleum jelly, high vacuum greases and water-based ultra-sonic couplants. However these may be difficult to remove subsequently.Distilled water can provide a very satisfactory coupling medium withoutsignificant end effects, and surface water may be removed subsequently bydrying. Manufacturers offer rubber-tipped transducers suitable for nonin-vasive measurements. With these transducers either good load control oraccurate determination of the rubber length is essential during measure-ment if good reproducibility is to be achieved.8.6 Bring transducer faces into intimate contact but do notexceed manufacturer’s recommended contact pressures.8.7 Follow the vendor’s instructions to adjust the instrumen-tation to match the transducer frequency to give good visualamplitude resolution.8.8 Determine T0, the travel time (zero correction) measuredin seconds, associated with the electronic circuits in thepulse-propagation instrument and coupling (Fig. 2(a)). Ensurethat the repeatability of the measurement is of sufficientprecision to meet the required accuracy in Young’s modulus.8.9 Adjust the gain of electronic components to give goodvisual amplitude resolution.8.10 Determine Tt, the total traverse time from the traces(Fig. 2(b)). Ensure that the repeatability of the measurement isof sufficient precision to meet the required accuracy in Young’smodulus.8.11 It is good practice to monitor the performance andreproducibility of the sonic velocity equipment by periodicallytesting a reference sample of similar material and geometry tothat typically used by the operator. This will monitor driftarising from deterioration in transducer performance. Stan-dards need to be representative of the material being tested andhave a similar geometry.9. Calculation9.1 Velocity of Signal:V 5LTt2 T02 Te(3)where:V = velocity of signal, m/s,L = specimen length, m,Tt= traverse time, s,T0= zero time, s, andTe= end correction time, s.9.2 Since graphites are not necessarily isotropic, the valueof Young’s modulus cannot be determined solely from aFIG. 1 Basic Experimental Arrangement for the Ultrasonic Pulsed-Wave Transit Time TechniqueC769 − 153velocity measurement in one direction. However, an approxi-mate Young’s modulus for each direction may be obtainedusing Eq 4 (based upon an assumed Poisson’s ratio of 0.2).More accurate estimates of the Young’s moduli require thedetermination of the full compliance matrix from a set ofmeasurements of longitudinal and shear wave velocities alongprincipal axes together with measurements of a sonic velocityat 45° to the principal axes.E 0.9 ρV2(4)where:E = Young’s modulus, Pa (approximate),ρ = density, kg/m3, andV = velocity of sound, m/s.9.3 Conversion Factors—See IEEE/ASTM SI 10.10. Report10.1 The report shall include the following:10.1.1 The wavelength or frequency of the transmitted pulseand sonic velocity equipment identification.NOTE 4—Due to the strong frequency dependent attenuation of ultra-sound in graphite, the frequency of the transmitted pulse may becompletely different from the nominal ultrasonic transducer frequency.10.1.2 Specimen dimensions, weight, and test specimenorientation with respect to forming direction.10.1.3 Sonic velocity for each specimen, along with adescription of the method of time of flight determination.10.1.4 Density of ea