1、Designation: C1259 14C1259 15Standard Test Method forDynamic Youngs Modulus, Shear Modulus, and PoissonsRatio for Advanced Ceramics by Impulse Excitation ofVibration1This standard is issued under the fixed designation C1259; the number immediately following the designation indicates the year oforigi
2、nal 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. Scope1.1 This test method covers determination of the dynamic elastic pro
3、perties of advanced ceramics at ambient temperatures.Specimens of these materials possess specific mechanical resonant frequencies that are determined by the elastic modulus, mass,and geometry of the test specimen. The dynamic elastic properties of a material can therefore be computed if the geometr
4、y, mass,and mechanical resonant frequencies of a suitable (rectangular, cylindrical, or disc geometry) test specimen of that material canbe measured. Dynamic Youngs modulus is determined using the resonant frequency in the flexural mode of vibration. Thedynamic shear modulus, or modulus of rigidity,
5、 is found using torsional resonant vibrations. Dynamic Youngs modulus anddynamic shear modulus are used to compute Poissons ratio.1.2 This test method measures the fundamental resonant frequency of test specimens of suitable geometry by exciting themmechanically by a singular elastic strike with an
6、impulse tool. Specimen supports, impulse locations, and signal pick-up points areselected to induce and measure specific modes of the transient vibrations. A transducer (for example, contact accelerometer ornon-contacting microphone) senses the resulting mechanical vibrations of the specimen and tra
7、nsforms them into electric signals.(See Fig. 1.) The transient signals are analyzed, and the fundamental resonant frequency is isolated and measured by the signalanalyzer, which provides a numerical reading that is (or is proportional to) either the frequency or the period of the specimenvibration.
8、The appropriate fundamental resonant frequencies, dimensions, and mass of the specimen are used to calculate dynamicYoungs modulus, dynamic shear modulus, and Poissons ratio.1.3 Although not specifically described herein, this test method can also be performed at cryogenic and high temperatures with
9、suitable equipment modifications and appropriate modifications to the calculations to compensate for thermal expansion, inaccordance with sections 9.2, 9.3, and 10.4 of C1198.1.4 Where possible, the procedures, sample specifications, and calculations in this test method are consistent with Test Meth
10、odsC623, C747, C848, and C1198.1.5 This test method uses test specimens in bar, rod, and disc geometries. The rod and bar geometries are described in the mainbody. The disc geometry is addressed in Annex A1.1.6 A modification of this test method can be used for quality control and nondestructive eva
11、luation, using changes in resonantfrequency to detect variations in specimen geometry and mass and internal flaws in the specimen. (See 5.5).1 This test method is under the jurisdiction of ASTM Committee C28 on Advanced Ceramics and is the direct responsibility of Subcommittee C28.01 on MechanicalPr
12、operties and Performance.Current edition approved Jan. 1, 2014Feb. 1, 2015. Published January 2014April 2015. Originally approved in 1994. Last previous edition approved in 20082014 asC1259 08.C1259 14. DOI: 10.1520/C1259-14.10.1520/C1259-15.FIG. 1 Block Diagram of Typical Test ApparatusThis documen
13、t is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Becauseit may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as app
14、ropriate. In all cases only the current versionof the standard as published by ASTM is to be considered the official document.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States11.7 The values stated in SI units are to be regarded as the
15、standard.1.8 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibilityof the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatorylimitations prior to use.2. Refer
16、enced Documents2.1 ASTM Standards:2C372 Test Method for Linear Thermal Expansion of Porcelain Enamel and Glaze Frits and Fired Ceramic Whiteware Productsby the Dilatometer MethodC623 Test Method for Youngs Modulus, Shear Modulus, and Poissons Ratio for Glass and Glass-Ceramics by ResonanceC747 Test
17、Method for Moduli of Elasticity and Fundamental Frequencies of Carbon and Graphite Materials by Sonic ResonanceC848 Test Method for Youngs Modulus, Shear Modulus, and Poissons Ratio For Ceramic Whitewares by ResonanceC1145 Terminology of Advanced CeramicsC1161 Test Method for Flexural Strength of Ad
18、vanced Ceramics at Ambient TemperatureC1198 Test Method for Dynamic Youngs Modulus, Shear Modulus, and Poissons Ratio for Advanced Ceramics by SonicResonanceD4092 Terminology for Plastics: Dynamic Mechanical PropertiesE6 Terminology Relating to Methods of Mechanical TestingE177 Practice for Use of t
19、he Terms Precision and Bias in ASTM Test MethodsE691 Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test MethodE2001 Guide for Resonant Ultrasound Spectroscopy for Defect Detection in Both Metallic and Non-metallic Parts3. Terminology3.1 Definitions:3.1.1 The defini
20、tions of terms relating to mechanical testing appearing in Terminology E6 should be considered as applying tothe terms used in this test method. The definitions of terms relating to advanced ceramics appearing in Terminology C1145 shouldbe considered as applying to the terms used in this test method
21、. Directly pertinent definitions as listed in Terminologies E6, C1145,and D4092 are shown in the following paragraphs with the appropriate source given in brackets.3.1.2 advanced ceramic, na highly engineered, high-performance, predominately nonmetallic, inorganic, ceramic materialhaving specific fu
22、nctional attributes. (C1145)3.1.3 dynamic mechanical measurement, na technique in which either the modulus or damping, or both, of a substance underoscillatory load or displacement is measured as a function of temperature, frequency, or time, or combination thereof. (D4092)3.1.4 elastic limit FL2,nt
23、he greatest stress that a material is capable of sustaining without permanent strain remaining uponcomplete release of the stress. (E6)3.1.5 elastic modulus FL2 , nthe ratio of stress to strain below the proportional limit. (E6)3.1.6 Poissons ratio () nd,nthe absolute value of the ratio of transvers
24、e strain to the corresponding axial strain resultingfrom uniformly distributed axial stress below the proportional limit of the material.3.1.6.1 DiscussionIn isotropic materials, Youngs Modulus (E), shear modulus (G), and Poissons ratio () are related by the following equation:5E/2G! 21 (1)(E6)3.1.7
25、 proportional limit FL2 , nthe greatest stress that a material is capable of sustaining without deviation fromproportionality of stress to strain (Hookes law). (E6)3.1.8 shear modulus (G) FL2 , nthe elastic modulus in shear or torsion. Also called modulus of rigidity or torsionalmodulus. (E6)3.1.9 Y
26、oungs modulus (E) FL2 , nthe elastic modulus in tension or compression. (E6)3.2 Definitions of Terms Specific to This Standard:3.2.1 antinodes, ntwo or more locations that have local maximum displacements, called antinodes, in an unconstrainedslender rod or bar in resonance. For the fundamental flex
27、ure resonance, the antinodes are located at the two ends and the centerof the specimen.2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at serviceastm.org. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary
28、 page on the ASTM website.C1259 1523.2.2 elastic, adjthe property of a material such that an application of stress within the elastic limit of that material makingup the body being stressed will cause an instantaneous and uniform deformation, which will be eliminated upon removal of thestress, with
29、the body returning instantly to its original size and shape without energy loss. Most advanced ceramics conform to thisdefinition well enough to make this resonance test valid.3.2.3 flexural vibrations, nthe vibrations that occur when the displacements in a slender rod or bar are in a plane normal t
30、othe length dimension.3.2.4 homogeneous, adjthe condition of a specimen such that the composition and density are uniform, so that any smallerspecimen taken from the original is representative of the whole. Practically, as long as the geometrical dimensions of the testspecimen are large with respect
31、 to the size of individual grains, crystals, components, pores, or microcracks, the body can beconsidered homogeneous.3.2.5 in-plane flexure, nfor rectangular parallelepiped geometries, a flexure mode in which the direction of displacement isin the major plane of the test specimen.3.2.6 isotropic, a
32、djthe condition of a specimen such that the values of the elastic properties are the same in all directions inthe material. Advanced ceramics are considered isotropic on a macroscopic scale, if they are homogeneous and there is a randomdistribution and orientation of phases, crystallites, components
33、, pores, or microcracks.3.2.7 nodes, none or more locations in a slender rod or bar in resonance having a constant zero displacement. For thefundamental flexural resonance of such a rod or bar, the nodes are located at 0.224 L from each end, where L is the length of thespecimen.3.2.8 out-of-plane fl
34、exure, nfor rectangular parallelepiped geometries, a flexure mode in which the direction of displacementis perpendicular to the major plane of the test specimen.3.2.9 resonant frequency, nnaturally occurring frequencies of a body driven into flexural, torsional, or longitudinal vibrationthat are det
35、ermined by the elastic modulus, mass, and dimensions of the body. The lowest resonant frequency in a given vibrationalmode is the fundamental resonant frequency of that mode.3.2.10 slender rod or bar, nin dynamic elastic property testing, a specimen whose ratio of length to minimum cross-sectionaldi
36、mension is at least 5 and preferably in the range of 20 to 25.3.2.11 torsional vibrations, nthe vibrations that occur when the oscillations in each cross-sectional plane of a slender rod orbar are such that the plane twists around the length dimension axis.4. Summary of Test Method4.1 This test meth
37、od measures the fundamental resonant frequency of test specimens of suitable geometry (bar, rod, or disc) byexciting them mechanically by a singular elastic strike with an impulse tool. A transducer (for example, contact accelerometer ornon-contacting microphone) senses the resulting mechanical vibr
38、ations of the specimen and transforms them into electric signals.Specimen supports, impulse locations, and signal pick-up points are selected to induce and measure specific modes of the transientvibrations. The signals are analyzed, and the fundamental resonant frequency is isolated and measured by
39、the signal analyzer,which provides a numerical reading that is (or is proportional to) either the frequency or the period of the specimen vibration. Theappropriate fundamental resonant frequencies, dimensions, and mass of the specimen are used to calculate dynamic Youngsmodulus, dynamic shear modulu
40、s, 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 appropriate for determining the modulus of advanced ceramics that are elastic,homogeneous
41、, and isotropic (1).35.3 This test method addresses the room temperature determination of dynamic moduli of elasticity of slender bars (rectangularcross-section) and rods (cylindrical). Flat plates and disks may also be measured similarly, but the required equations fordetermining the moduli are not
42、 addressed herein.5.4 This dynamic test method has several advantages and differences from static loading techniques and from resonanttechniques requiring continuous excitation.5.4.1 The test method is nondestructive in nature and can be used for specimens prepared for other tests. The specimens are
43、subjected to minute strains; hence, the moduli are measured at or near the origin of the stress-strain curve, with the minimumpossibility of fracture.5.4.2 The impulse excitation test uses an impact tool and simple supports for the test specimen. There is no requirement forcomplex support systems th
44、at require elaborate setup or alignment.3 The boldface numbers in parentheses refer to the list of references at the end of this test method.C1259 1535.5 This technique can be used to measure resonant frequencies alone for the purposes of quality control and acceptance of testspecimens of both regul
45、ar and complex shapes. A range of acceptable resonant frequencies is determined for a specimen with aparticular geometry and mass. Deviations in specimen dimensions or mass and internal flaws (cracks, delaminations,inhomogeneities, porosity, etc) will change the resonant frequency for that specimen.
46、 Any specimen with a resonant frequencyfalling outside the prescribed frequency range is rejected. The actual modulus of each specimen need not be determined as longas the limits of the selected frequency range are known to include the resonant frequency that the specimen must possess if itsgeometry
47、 and mass and internal structure are within specified tolerances. The technique is particularly suitable for testingspecimens with complex geometries (other than parallelepipeds, cylinders/rods, or discs) that would not be suitable for testing byother procedures. This is similar to the evaluation me
48、thod described in Guide E2001.5.6 If a thermal treatment or an environmental exposure affects the elastic response of the test specimen, this test method maybe suitable for the determination of specific effects of thermal history, environment exposure, etc. Specimen descriptions shouldinclude any sp
49、ecific thermal treatments or environmental exposures that the specimens have received.6. Interferences6.1 The relationships between resonant frequency and dynamic modulus presented herein are specifically applicable tohomogeneous, elastic, isotropic materials.6.1.1 This method of determining the moduli is applicable to composite ceramics and inhomogeneous materials only withcareful consideration of the effect of inhomogeneities and anisotropy. The character (volume fraction, size, morphology,distribution, orientation
