1、Designation: C 1198 01Standard Test Method forDynamic Youngs Modulus, Shear Modulus, and PoissonsRatio for Advanced Ceramics by Sonic Resonance1This standard is issued under the fixed designation C 1198; the number immediately following the designation indicates the year oforiginal adoption or, in t
2、he 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 determination of the dy-namic elastic properties of adva
3、nced ceramics. Specimens ofthese materials possess specific mechanical resonant frequen-cies that are determined by the elastic modulus, mass, andgeometry of the test specimen. Therefore, the dynamic elasticproperties of a material can be computed if the geometry, mass,and mechanical resonant freque
4、ncies of a suitable test speci-men of that material can be measured. Dynamic Youngsmodulus is determined using the resonant frequency in theflexural mode of vibration. The dynamic shear modulus, ormodulus of rigidity, is found using torsional resonant vibra-tions. Dynamic Youngs modulus and dynamic
5、shear modulusare used to compute Poissons ratio.1.2 This test method is specifically appropriate for advancedceramics that are elastic, homogeneous, and isotropic (1).2Advanced ceramics of a composite character (particulate,whisker, or fiber reinforced) may be tested by this test methodwith the unde
6、rstanding that the character (volume fraction,size, morphology, distribution, orientation, elastic properties,and interfacial bonding) of the reinforcement in the testspecimen will have a direct effect on the elastic properties.These reinforcement effects must be considered in interpretingthe test r
7、esults for composites. This test method is notsatisfactory for specimens that have cracks or voids that aremajor discontinuities in the specimen. Neither is the testmethod satisfactory when these materials cannot be fabricatedin a uniform rectangular or circular cross section.1.3 A high-temperature
8、furnace and cryogenic cabinet aredescribed for measuring the dynamic elastic moduli as afunction of temperature from 195 to 1200C.1.4 Modification of this test method for use in qualitycontrol is possible. A range of acceptable resonant frequenciesis determined for a specimen with a particular geome
9、try andmass. Any specimen with a frequency response falling outsidethis frequency 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 geometr
10、y andmass are within specified tolerances.1.5 The procedures in this test method are, where possible,consistent with the procedures of Test Methods C 623, C 747,and C 848. The tables of these test methods have been replacedby the actual formulas from the original references. With theadvent of comput
11、ers and sophisticated hand calculators, theactual formulas can be easily used and provide greater accu-racy than factor tables.1.6 The values stated in SI units are to be regarded as thestandard. The values given in parentheses are for informationonly.1.7 This standard does not purport to address al
12、l 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:C 372 Test Method for
13、 Linear Thermal Expansion of Por-celain Enamel and Glaze Frits and Fired Ceramic Whitew-are Products by the Dilatomer Method3C 623 Test Method for Youngs Modulus, Shear Modulus,and Poissons Ratio for Glass and Glass-Ceramics byResonance3C 747 Test Method for Moduli of Elasticity and Fundamen-tal Fre
14、quencies of Carbon and Graphite Materials by SonicResonance4C 848 Test Method for Youngs Modulus, Shear Modulus,and Poissons Ratio for Ceramic Whitewares by Reso-nance3C 1145 Terminology of Advanced Ceramics4C 1161 Test Method for Flexural Strength of Advanced1This test method is under the jurisdict
15、ion of ASTM Committee C28 onAdvanced Ceramics and is the direct responsibility of Subcommittee C28.01 onMechanical Properties and Performance.Current edition approved April 10, 2001. Published June 2001. Originallypublished as C 1198 91. Last previous edition C 1198 96.2The boldface numbers given in
16、 parentheses refer to a list of references at theend of the text.3Annual Book of ASTM Standards, Vol 15.02.4Annual Book of ASTM Standards, Vol 15.01.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.Ceramics at Ambient Temperatures4D 4
17、092 Terminology Relating to Dynamic MechanicalMeasurements on Plastics53. Terminology3.1 Definitions:3.1.1 advanced ceramic, na highly engineered, high per-formance, predominately nonmetallic, inorganic, ceramic ma-terial having specific functional attributes. (C 1145)3.1.1.1 dynamic mechanical meas
18、urement, na techniquein which either the modulus or damping, or both, of a substanceunder oscillatory load or displacement is measured as afunction of temperature, frequency, or time, or combinationthereof. (D 4092)3.1.2 elastic limit FL2, nthe greatest stress that amaterial is capable of sustaining
19、 without permanent strainremaining upon complete release of the stress.3.1.3 elastic modulus FL2, nthe ratio of stress to strainbelow the proportional limit.3.1.4 Poissons ratio () nd, nthe absolute value of theratio of transverse strain to the corresponding axial strainresulting from uniformly dist
20、ributed 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 ! 2 13.1.5 proportional limit FL2, nthe greatest stress that amaterial is capable of su
21、staining without deviation fromproportionality of stress to strain (Hookes law).3.1.6 shear modulus (G) FL2, nthe elastic modulus inshear or torsion. Also called modulus of rigidity or torsionalmodulus.3.1.7 Youngs modulus ( E) FL2, nthe elastic modulusin tension or compression.3.2 Definitions of Te
22、rms Specific to This Standard:3.2.1 anti-nodes, nan unconstrained slender rod or bar inresonance contains two or more locations that have localmaximum displacements, called anti-nodes. For the fundamen-tal flexure resonance, the anti-nodes are located at the two endsand the center of the specimen.3.
23、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, that will be eliminated upon removalof the stress, with the body returning instantly to its orig
24、inalsize and shape without energy loss. Most advanced ceramicsconform to this definition well enough to make this resonancetest valid.3.2.3 flexural vibrations, nthe vibrations that occur whenthe oscillations in a slender rod or bar are in the plane normalto the length dimension.3.2.4 homogeneous, a
25、djthe condition of a specimen suchthat the composition and density are uniform, such 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
26、, or components, the body can be consideredhomogeneous.3.2.5 isotropic, adjthe condition of a specimen such thatthe values of the elastic properties are the same in all directionsin the material.Advanced ceramics are considered isotropic ona macroscopic scale, if they are homogeneous and there is ar
27、andom distribution and orientation of phases, crystallites, andcomponents.3.2.6 nodes, na slender rod or bar in resonance containsone or more locations having a constant zero displacement,called nodes. For the fundamental flexural resonance, the nodesare located at 0.224 L from each end, where L is
28、the length ofthe specimen.3.2.7 resonance, na slender rod or bar driven into one ofthe modes of vibration described in 3.2.3 or 3.2.9 is said to bein resonance when the imposed frequency is such that theresultant displacements for a given amount of driving force areat a maximum. The resonant frequen
29、cies are natural vibrationfrequencies that are determined by the elastic modulus, mass,and dimensions of the test specimen.3.2.8 slender rod or bar, nin dynamic elastic propertytesting, a specimen whose ratio of length to minimum cross-sectional dimension is at least five and preferably in the range
30、of 20 to 25.3.2.9 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.4. Summary of Test Method4.1 This test method measures the resonant frequencies oftest specimen
31、s of suitable geometry by exciting them atcontinuously variable frequencies. Mechanical excitation ofthe bars is provided through the use of a transducer thattransforms a cyclic electrical signal into a cyclic mechanicalforce on the specimen.Asecond transducer senses the resultingmechanical vibratio
32、ns of the specimen and transforms theminto an electrical signal. The amplitude and frequency of thesignal are measured by an oscilloscope or other means to detectresonance. The resonant frequencies, dimensions, and mass ofthe specimen are used to calculate dynamic Youngs modulusand dynamic shear mod
33、ulus.5. Significance and Use5.1 This test method may be used for material development,characterization, design data generation, and quality controlpurposes. It is specifically appropriate for determining themodulus of advanced ceramics that are elastic, homogeneous,and isotropic.5.1.1 This test meth
34、od is nondestructive in nature. Onlyminute stresses are applied to the specimen, thus minimizingthe possibility of fracture.5.1.2 The period of time during which measurement stressis applied and removed is of the order of hundreds ofmicroseconds. With this test method it is feasible to performmeasur
35、ements at high temperatures, where delayed elastic and5Annual Book of ASTM Standards, Vol 08.02.C1198012creep effects would invalidate modulus measurements calcu-lated from static loading.5.2 This test method has advantages in certain respects overthe use of static loading systems for measuring modu
36、li inadvanced ceramics. It is nondestructive in nature and can beused for specimens prepared for other tests. Specimens aresubjected to minute strains; hence, the moduli are measured ator near the origin of the stress-strain curve with the minimumpossibility of fracture. The period of time during wh
37、ichmeasurement stress is applied and removed is of the order ofhundreds of microseconds. With this test method it is feasibleto perform measurements at high temperatures, where delayedelastic and creep effects would invalidate modulus measure-ments calculated from static loading.6. Interferences6.1
38、The relationships between resonant frequency and dy-namic modulus presented herein are specifically applicable tohomogeneous, elastic, isotropic materials.6.1.1 This test method of determining the moduli is appli-cable to composite ceramics and inhomogeneous materialsonly with careful consideration
39、of the effect of inhomogeneitiesand anisotropy. The character (volume fraction, size, morphol-ogy, distribution, orientation, elastic properties, and interfacialbonding) of the reinforcement/inhomogeneities in the speci-mens will have a direct effect on the elastic properties of thespecimen as a who
40、le. These effects must be considered ininterpreting the test results for composites and inhomogeneousmaterials.6.1.2 If specific surface treatments (coatings, machining,grinding, etching, etc.) change the elastic properties of thenear-surface material, there will be accentuated effects on thepropert
41、ies measured by this flexural method, as compared tostatic/bulk measurements by tensile or compression testing.6.1.3 This 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 li
42、mited tospecimens with regular geometries (rectangular parallelepipedand cylinders) for which analytical equations are available torelate geometry, mass, and modulus to the resonant vibrationfrequencies. This test method is not appropriate for determin-ing the elastic properties of materials which c
43、annot be fabri-cated into such geometries.6.2.1 The analytical equations assume parallel/concentricdimensions for the regular geometries of the specimen. Devia-tions from the specified tolerances for the dimensions of thespecimens will change the resonant frequencies and introduceerror into the calc
44、ulations.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 C 1161 willchange the resonant frequency of the test bars and introduceerror into the calculations of the dynamic modulus. It isrecom
45、mended that specimens for this test not have chamferedor rounded edges. Alternately, if narrow rectangular specimenswith chamfers or edge radii are tested, then the procedures inAnnex A1 should be used to correct the calculated Youngsmodulus, E.6.2.3 For specimens with as-fabricated/rough or unevens
46、urfaces, variations in dimension can have a significant effectin the calculations. For example, in the calculation of thedynamic modulus, the modulus value is inversely proportionalto the cube of the thickness. Uniform specimen dimensions andprecise measurements are essential for accurate results.7.
47、 Apparatus7.1 The test apparatus is shown in Fig. 1. It consists of avariable-frequency audio oscillator, used to generate a sinusoi-dal voltage, and a power amplifier and suitable transducer toconvert the electrical signal to a mechanical driving vibration.A frequency meter (preferably digital) mon
48、itors the audiooscillator output to provide an accurate frequency determina-tion. A suitable suspension-coupling system supports the testspecimen. Another transducer acts to detect mechanical vibra-tion in the specimen and to convert it into an electrical signalthat is passed through an amplifier an
49、d displayed on anindicating meter. The meter may be a voltmeter, microamme-ter, or oscilloscope. An oscilloscope is recommended becauseit enables the operator to positively identify resonances,including higher order harmonics, by Lissajous figure analysis.If a Lissajous figure is desired, the output of the oscillator isalso coupled to the horizontal plates of the oscilloscope. Iftemperature-dependent data are desired, a suitable furnace orcryogenic chamber is used. Details of the equipment are asfollows:7.2 Audio Oscillator, ha
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