1、Designation: C 1259 01Standard 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 or cylindrical geometry)test specimen of that material can be measured. DynamicYoungs modulus is determined using the resonant frequencyin the flexural mode of vibration. The dynamic shear modulus,or modulus of rigidity, is found usin
5、g torsional resonantvibrations. Dynamic Youngs modulus and dynamic shearmodulus are used to compute Poissons ratio.1.2 Although not specifically described herein, this testmethod can also be performed at cryogenic and high tempera-tures with suitable equipment modifications and appropriatemodificati
6、ons to the calculations to compensate for thermalexpansion.1.3 Where possible, the procedures, sample specifications,and calculations in this test method are consistent with TestMethods C 623, C 747, C 848, and C 1198.1.4 This test method uses test specimens in bar, rod, anddisc geometries. The rod
7、and bar geometries are described inthe main body. The disc geometry is addressed in Annex A1.1.5 The values stated in SI units are to be regarded as thestandard.1.6 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the us
8、er 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 Linear Thermal Expansion of Por-celain Enamel and Glaze Frits and Fired Ceramic Whitew-are
9、 Products by the Dilatometer Method2C 623 Test Method for Youngs Modulus, Shear Modulus,and Poissons Ratio for Glass and Glass-Ceramics byResonance2C 747 Test Method for Moduli of Elasticity and Fundamen-tal Frequencies of Carbon and Graphite Materials by SonicResonance3C 848 Test Method for Youngs
10、Modulus, Shear Modulus,and Poissons Ratio for Ceramic Whitewares by Reso-nance2C 1145 Terminology of Advanced Ceramics3C 1161 Test Method for Flexural Strength of AdvancedCeramics at Ambient Temperature3C 1198 Test Method for Dynamic Youngs Modulus, ShearModulus, and Poissons Ratio for Advanced Cera
11、mics bySonic Resonance3D 4092 Terminology Relating to Dynamic MechanicalMeasurements on Plastics4E 6 Terminology Relating to Methods of Mechanical Test-ing5E 177 Practice for Use of the Terms Precision and Bias inASTM Test Methods3E 691 Practice for Conducting an Interlaboratory Study toDetermine th
12、e Precision of a Test Method63. Terminology3.1 DefinitionsThe definitions of terms relating to me-chanical testing appearing in Terminology E 6 should beconsidered as applying to the terms used in this test method.The definitions of terms relating to advanced ceramics appear-ing in Terminology C 114
13、5 should be considered as applying tothe terms used in this test method. Directly pertinent definitionsas listed in Terminologies E 6, C 1145, and D 4092 are shownin the following paragraphs with the appropriate source givenin brackets.3.1.1 advanced ceramic, na highly engineered, high-performance,
14、predominately nonmetallic, inorganic, ceramic1This test method is under the jurisdiction of ASTM Committee C28 onAdvanced Ceramics and is the direct responsibility of Subcommittee C28.01 onProperties and Performance.Current edition approved April 10, 2001. Published June 2001. Originallypublished as
15、 C 125994. Last previous edition C 125998.2Annual Book of ASTM Standards, Vol 15.02.3Annual Book of ASTM Standards, Vol 15.01.4Annual Book of ASTM Standards, Vol 08.02.5Annual Book of ASTM Standards, Vol 03.01.6Annual Book of ASTM Standards, Vol 14.02.1Copyright ASTM, 100 Barr Harbor Drive, West Con
16、shohocken, PA 19428-2959, United States.material having specific functional attributes. (C 1145)3.1.2 dynamic mechanical measurement, na technique inwhich either the modulus or damping, or both, of a substanceunder oscillatory load or displacement is measured as afunction of temperature, frequency,
17、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 complete release of the stress. (E 6)3.1.4 elastic modulus FL2, nthe ratio of stress to strainbelow the proportional limit. (E 6)3.1.5
18、Poissons ratio () nd, nthe absolute value of theratio of transverse strain to the corresponding axial strainresulting from uniformly distributed axial stress below theproportional limit of the material.3.1.5.1 DiscussionIn isotropic materials, Youngs Modu-lus (E), shear modulus (G), and Poissons rat
19、io () are relatedby the following equation: 5 E/2G! 1 (1)(E 6)3.1.6 proportional limit FL2, nthe greatest stress that amaterial is capable of sustaining without deviation fromproportionality of stress to strain (Hookes law). (E 6)3.1.7 shear modulus (G) FL2, nthe elastic modulus inshear or torsion.
20、Also called modulus of rigidity or torsionalmodulus. (E 6)3.1.8 Youngs modulus (E) FL2, nthe elastic modulus intension or compression. (E 6)3.2 Definitions of Terms Specific to This Standard:3.2.1 antinodes, ntwo or more locations that have localmaximum displacements, called anti-nodes, in an uncon-
21、strained slender rod or bar in resonance. For the fundamentalflexure resonance, the anti-nodes are located at the two endsand the center of the specimen.3.2.2 elastic, adjthe property of a material such that anapplication of stress within the elastic limit of that materialmaking up the body being st
22、ressed 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 energy loss. Most advancedceramics conform to this definition well enough to make thisresonance test valid.3.2.3 flex
23、ural 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 specimen suchthat the composition and density are uniform, so that anysmaller specimen taken from the original is representa
24、tive 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 microcracks, the bodycan be considered homogeneous.3.2.5 in-plane flexure, nfor rectangular parallelepipedgeometries, a fle
25、xure 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 properties are the same in all directionsin the material. Advanced ceramics are considered isotropic ona macroscopic scale,
26、if they are homogeneous and there is arandom distribution and orientation of phases, crystallites,components, pores, or microcracks.3.2.7 nodes, na slender rod or bar in resonance containingone or more locations having a constant zero displacement. Forthe fundamental flexural resonance of such a rod
27、 or bar, thenodes are located at 0.224 L from each end, where L is thelength of the specimen.3.2.8 out-of-plane flexure, nfor rectangular parallelepipedgeometries, a flexure mode in which the direction of displace-ment is perpendicular to the major plane of the test specimen.3.2.9 resonant frequency
28、, 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 lowest resonant frequency in agiven vibrational mode is the fundamental resonant frequencyof that mode.3.2.10 slend
29、er rod 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
30、 bar 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 by excitingthem mechanically by a singular elastic strike with an impulsetool. A transducer (for example
31、, contact accelerometer ornon-contacting microphone) senses the resulting mechanicalvibrations of the specimen and transforms them into electricsignals. Specimen supports, impulse locations, and signalpick-up points are selected to induce and measure specificmodes of the transient vibrations. The si
32、gnals are analyzed, andthe fundamental resonant frequency is isolated and measuredby the signal analyzer, which provides a numerical reading thatis (or is proportional to) either the frequency or the period ofthe specimen vibration. The appropriate fundamental resonantfrequencies, dimensions, and ma
33、ss of the specimen are used tocalculate 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 is specifically appropr
34、iate for deter-mining the modulus of advanced ceramics that are elastic,homogeneous, and isotropic (1).75.3 This test method addresses the room temperature deter-mination of dynamic moduli of elasticity of slender bars(rectangular cross-section) and rods (cylindrical). Flat plates7The boldface numbe
35、rs in parentheses refer to the list of references at the end ofthis test method.C 12592and 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 techni
36、ques and from resonanttechniques requiring continuous excitation.5.4.1 The test method 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
37、 the minimumpossibility of fracture.5.4.2 The impulse excitation test uses an impact 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 th
38、e purposes of quality control and acceptance oftest specimens of both regular and complex shapes. A range ofacceptable resonant frequencies is determined for a specimenwith a particular geometry and mass. The technique is particu-larly suitable for testing specimens with complex geometries(other tha
39、n parallelepipeds, cylinders/rods, or discs) that wouldnot be suitable for testing by other procedures. Any specimenwith a frequency response falling outside the prescribedfrequency range is rejected. The actual modulus of eachspecimen need not be determined as long as the limits of theselected freq
40、uency range are known to include the resonantfrequency that the specimen must possess if its geometry andmass are within specified tolerances.5.6 If a thermal treatment or an environmental exposureaffects the elastic response of the test specimen, this testmethod may be suitable for the determinatio
41、n of specific effectsof thermal history, environment exposure, etc. Specimen de-scriptions should include any specific thermal treatments orenvironmental exposures that the specimens have received.6. Interferences6.1 The relationships between resonant frequency and dy-namic modulus presented herein
42、are specifically applicable tohomogeneous, elastic, isotropic materials.6.1.1 This method of determining the moduli is applicableto composite ceramics and inhomogeneous materials only withcareful consideration of the effect of inhomogeneities andanisotropy. The character (volume fraction, size, morp
43、hology,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 in
44、homogeneousmaterials.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
45、If specific surface treatments (coatings, machining,grinding, etching, etc.) change the elastic properties of thenear-surface material, there will be accentuated effects on theproperties measured by this flexural method, as compared tostatic/bulk measurements by tensile or compression testing.6.1.4
46、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 parallelepiped,cylinders, and discs) for which analytical equat
47、ions are avail-able to relate geometry, mass, and modulus to the resonantvibration frequencies. The test method is not appropriate fordetermining the elastic properties of materials that cannot befabricated into such geometries.6.2.1 The analytical equations assume parallel and concen-tric dimension
48、s 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
49、 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 isrecommended that specimens for this test method not havechamfered or rounded edges. Alternately, if narrow rectangularspecimens with chamfers or edge radii are tested, then theprocedures in Annex A2 should be used to correct the calcu-lated Youngs modulus, E.6.2.3 For specimens with as-fabricated and rough or unevensurfaces, variations in dime
