1、Designation: C 1259 08Standard Test Method forDynamic Youngs Modulus, Shear Modulus, and PoissonsRatio for Advanced Ceramics by Impulse Excitation ofVibration1This standard is issued under the fixed designation C 1259; the number immediately following the designation indicates the year oforiginal ad
2、option 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 determination of the dynamicelastic propertie
3、s of advanced ceramics at ambient tempera-tures. Specimens of these materials possess specific mechani-cal resonant frequencies that are determined by the elasticmodulus, mass, and geometry of the test specimen. Thedynamic elastic properties of a material can therefore becomputed if the geometry, ma
4、ss, and mechanical resonantfrequencies of a suitable (rectangular, cylindrical, or discgeometry) test specimen of that material can be measured.Dynamic Youngs modulus is determined using the resonantfrequency in the flexural mode of vibration. The dynamic shearmodulus, or modulus of rigidity, is fou
5、nd using torsionalresonant vibrations. Dynamic Youngs modulus and dynamicshear modulus are used to compute Poissons ratio.1.2 This test method measures the fundamental resonantfrequency of test specimens of suitable geometry by excitingthem mechanically by a singular elastic strike with an impulseto
6、ol. Specimen supports, impulse locations, and signal pick-uppoints are selected to induce and measure specific modes of thetransient vibrations. A transducer (for example, contact accel-erometer or non-contacting microphone) senses the resultingmechanical vibrations of the specimen and transforms th
7、eminto electric signals. (See Fig. 1.) The transient 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 approp
8、riate funda-mental resonant frequencies, dimensions, and mass of thespecimen are used to calculate dynamic Youngs modulus,dynamic shear modulus, and Poissons ratio.1.3 Although not specifically described herein, this testmethod can also be performed at cryogenic and high tempera-tures with suitable
9、equipment modifications and appropriatemodifications to the calculations to compensate for thermalexpansion, in accordance with sections 9.2, 9.3, and 10.4 ofC 1198.1.4 Where possible, the procedures, sample specifications,and calculations in this test method are consistent with TestMethods C 623, C
10、 747, C 848, and C 1198.1.5 This test method uses test specimens in bar, rod, anddisc geometries. The rod and bar geometries are described inthe main body. The disc geometry is addressed in Annex A1.1.6 A modification of this test method can be used forquality control and nondestructive evaluation,
11、using changes inresonant frequency to detect variations in specimen geometryand mass and internal flaws in the specimen. (See 5.5).1.7 The values stated in SI units are to be regarded as thestandard.1.8 This standard does not purport to address all of thesafety concerns, if any, associated with its
12、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:2C 372 Test Method for Linear Thermal Expansion of Por-celain Enamel and G
13、laze Frits and Fired Ceramic Whitew-are Products by the Dilatometer Method1This test method is under the jurisdiction of ASTM Committee C28 onAdvanced Ceramics and is the direct responsibility of Subcommittee C28.01 onMechanical Properties and PerformanceCurrent edition approved Jan. 1, 2008. Publis
14、hed January 2008. Originallyapproved in 1994. Last previous edition approved in 2001 as C 125901.2For 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 Docum
15、ent Summary page onthe ASTM website.FIG. 1 Block Diagram of Typical Test Apparatus1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.Copyright by ASTM Intl (all rights reserved); Wed Jun 4 20:30:10 EDT 2008Downloaded/printed byGuo Dehua
16、 (CNIS) pursuant to License Agreement. No further reproductions authorized.C 623 Test Method for Youngs Modulus, Shear Modulus,and Poissons Ratio for Glass and Glass-Ceramics byResonanceC 747 Test Method for Moduli of Elasticity and Fundamen-tal Frequencies of Carbon and Graphite Materials by SonicR
17、esonanceC 848 Test Method for Youngs Modulus, Shear Modulus,and Poissons Ratio For Ceramic Whitewares by Reso-nanceC 1145 Terminology of Advanced CeramicsC 1161 Test Method for Flexural Strength of AdvancedCeramics at Ambient TemperatureC 1198 Test Method for Dynamic Youngs Modulus, ShearModulus, an
18、d Poissons Ratio for Advanced Ceramics bySonic ResonanceD 4092 Terminology for Plastics: Dynamic MechanicalPropertiesE6 Terminology Relating to Methods of Mechanical Test-ingE 177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE 691 Practice for Conducting an Interlaboratory Stu
19、dy toDetermine the Precision of a Test MethodE 2001 Guide for Resonant Ultrasound Spectroscopy forDefect Detection in Both Metallic and Non-metallic Parts3. Terminology3.1 DefinitionsThe definitions of terms relating to me-chanical testing appearing in Terminology E6 should beconsidered as applying
20、to the terms used in this test method.The definitions of terms relating to advanced ceramics appear-ing in Terminology C 1145 should be considered as applying tothe terms used in this test method. Directly pertinent definitionsas listed in Terminologies E6, C 1145, and D 4092 are shownin the followi
21、ng paragraphs with the appropriate source givenin brackets.3.1.1 advanced ceramic, na highly engineered, high-performance, predominately nonmetallic, inorganic, ceramicmaterial having specific functional attributes. (C 1145)3.1.2 dynamic mechanical measurement, na technique inwhich either the modulu
22、s or damping, or both, of a substanceunder oscillatory load or displacement is measured as afunction of temperature, frequency, or time, or combinationthereof. (D 4092)3.1.3 elastic limit FL2, nthe greatest stress that amaterial is capable of sustaining without permanent strainremaining upon complet
23、e release of the stress. (E6)3.1.4 elastic modulus FL2, nthe ratio of stress to strainbelow the proportional limit. (E6)3.1.5 Poissons ratio () nd, nthe absolute value of theratio of transverse strain to the corresponding axial strainresulting from uniformly distributed axial stress below theproport
24、ional limit of the material.3.1.5.1 DiscussionIn isotropic materials, Youngs Modu-lus (E), shear modulus (G), and Poissons ratio () are relatedby the following equation: 5 E/2G! 1 (1)(E6)3.1.6 proportional limit FL2, nthe greatest stress that amaterial is capable of sustaining without deviation from
25、proportionality of stress to strain (Hookes law). (E6)3.1.7 shear modulus (G) FL2, nthe elastic modulus inshear or torsion. Also called modulus of rigidity or torsionalmodulus. (E6)3.1.8 Youngs modulus (E) FL2, nthe elastic modulus intension or compression. (E6)3.2 Definitions of Terms Specific to T
26、his 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 located at the two ends and thecenter of the specimen.3.2.2 elastic, adjthe propert
27、y 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 stress, with the body returning instantly to itsoriginal size and shape without
28、 energy loss. Most advancedceramics conform to this definition well enough to make thisresonance test valid.3.2.3 flexural vibrations, nthe vibrations that occur whenthe displacements in a slender rod or bar are in a plane normalto the length dimension.3.2.4 homogeneous, adjthe condition of a specim
29、en 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 respect to the size of individualgrains, crystals, components, pores, or micro
30、cracks, 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 isotropic, adjthe condition of a specimen such thatthe values of the elastic proper
31、ties are the same in all directionsin the material. Advanced ceramics are considered isotropic ona macroscopic scale, if they are homogeneous and there is arandom distribution and orientation of phases, crystallites,components, pores, or microcracks.3.2.7 nodes, none or more locations in a slender r
32、od orbar in 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.3.2.8 out-of-plane flexure, nfor rectangular parallelepipedgeometries, a flexure mode in which th
33、e direction of displace-ment is perpendicular to the major plane of the test specimen.3.2.9 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 lowes
34、t resonant frequency in agiven vibrational mode is the fundamental resonant frequencyof that mode.C1259082Copyright by ASTM Intl (all rights reserved); Wed Jun 4 20:30:10 EDT 2008Downloaded/printed byGuo Dehua (CNIS) pursuant to License Agreement. No further reproductions authorized.3.2.10 slender r
35、od 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 range of20 to 25.3.2.11 torsional vibrations, nthe vibrations that occurwhen the oscillations in each cross-sectional plane of a slenderrod or bar
36、 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 (bar, rod, ordisc) by exciting them mechanically by a singular elastic strikewith an impulse tool. A transdu
37、cer (for example, contactaccelerometer or non-contacting microphone) senses the result-ing mechanical vibrations of the specimen and transforms theminto electric signals. Specimen supports, impulse locations, andsignal pick-up points are selected to induce and measurespecific modes of the transient
38、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 frequenci
39、es, dimensions, and mass of thespecimen are used to calculate 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.5.2 This test method i
40、s specifically appropriate for deter-mining the modulus of advanced ceramics 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 (cylindrical). Flat pla
41、tesand 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.5.4.1 The test meth
42、od 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 test uses an impact
43、 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 both regular and co
44、mplex shapes. A range ofacceptable resonant frequencies is determined for a specimenwith a particular geometry and mass. Deviations in specimendimensions or mass and internal flaws (cracks, delaminations,inhomogeneities, porosity, etc) will change the resonant fre-quency for that specimen. Any speci
45、men with a resonantfrequency falling outside the prescribed frequency range isrejected. The actual modulus of each specimen need not bedetermined as long as the limits of the selected frequency rangeare known to include the resonant frequency that the specimenmust possess if its geometry and mass an
46、d internal structure arewithin specified tolerances. The technique is particularly suit-able for testing specimens with complex geometries (other thanparallelepipeds, cylinders/rods, or discs) that would not besuitable for testing by other procedures. This is similar to theevaluation method describe
47、d in Guide E 2001.5.6 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, etc. Specimen de-scriptions should include any specific therm
48、al treatments orenvironmental exposures that the specimens have received.6. 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 appli
49、cableto composite ceramics and inhomogeneous materials only withcareful consideration of the effect of inhomogeneities andanisotropy. The character (volume fraction, size, morphology,distribution, orientation, elastic properties, and interfacialbonding) of the reinforcement and inhomogeneities in thespecimens will have a direct effect on the elastic properties ofthe specimen as a whole. These effects must be considered ininterpreting the test results for composites and inhomogeneousmaterials.6.1.2 The procedure involves m
