1、Designation: C1259 081C1259 14Standard 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 oforig
2、inal 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 NOTEAdded research report footnote to Section 12.2 editorially in April 2
3、009.1. Scope1.1 This test method covers determination of the dynamic elastic properties 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 d
4、ynamic elastic properties of a material can therefore be computed if the geometry, 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 t
5、he flexural mode of vibration. Thedynamic shear modulus, or modulus of rigidity, 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 suit
6、able geometry by exciting themmechanically by a singular elastic strike with an 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-contactin
7、g microphone) senses the resulting mechanical vibrations of the specimen and transforms 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 i
8、s proportional to) either the frequency or the period of the specimenvibration. 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
9、, this test method can also be performed at cryogenic and high temperatures withsuitable 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 sp
10、ecifications, and calculations in this test method are consistent with Test MethodsC623, 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 This test m
11、ethod is under the jurisdiction of ASTM Committee C28 on Advanced Ceramics and is the direct responsibility of Subcommittee C28.01 on MechanicalProperties and PerformanceCurrent edition approved Jan. 1, 2008Jan. 1, 2014. Published January 2008 January 2014. Originally approved in 1994. Last previous
12、 edition approved in 20012008 asC1259 01.C1259 08. DOI: 10.1520/C1259-08E01.10.1520/C1259-14.FIG. 1 Block Diagram of Typical Test ApparatusThis document 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 v
13、ersion. Becauseit may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current versionof the standard as published by ASTM is to be considered the official document.Copyright ASTM Internat
14、ional, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States11.6 A modification of this test method can be used for quality control and nondestructive evaluation, using changes in resonantfrequency to detect variations in specimen geometry and mass and internal flaws in
15、 the specimen. (See 5.5).1.7 The values stated in SI units are to be regarded as the 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 pra
16、ctices and determine the applicability of regulatorylimitations prior to use.2. Referenced 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,
17、Shear Modulus, and Poissons Ratio for Glass and Glass-Ceramics by ResonanceC747 Test 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 Resonan
18、ceC1145 Terminology of Advanced CeramicsC1161 Test Method for Flexural Strength of Advanced 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 Propert
19、iesE6 Terminology Relating to Methods of Mechanical TestingE177 Practice for Use of the 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
20、in Both Metallic and Non-metallic Parts3. Terminology3.1 Definitions:3.1.1 The definitions 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 Te
21、rminology C1145 shouldbe considered as applying to the terms used in this test method. 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-
22、performance, predominately nonmetallic, inorganic, ceramic materialhaving specific functional 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 tempe
23、rature, frequency, or time, or combination thereof. (D4092)3.1.4 elastic limit FL2,nthe 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 proportiona
24、l limit. (E6)3.1.6 Poissons ratio () nd,nthe absolute value of the ratio of transverse 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
25、), and Poissons ratio () are related by the following equation:5E/2G! 21 (1)(E6)3.1.7 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
26、in shear or torsion. Also called modulus of rigidity or torsionalmodulus. (E6)3.1.9 Youngs modulus (E) FL2 , nthe elastic modulus in tension or compression. (E6)3.2 Definitions of Terms Specific to This Standard:2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Cust
27、omer Service at serviceastm.org. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary page on the ASTM website.C1259 1423.2.1 antinodes, ntwo or more locations that have local maximum displacements, called antinodes, in an unconstrainedslender rod or bar in re
28、sonance. For the fundamental flexure resonance, the antinodes are located at the two ends and the centerof the specimen.3.2.2 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 instantaneo
29、us and uniform deformation, which will be eliminated upon removal of thestress, with 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 vibrati
30、ons that occur when the displacements in a slender rod or bar are in a plane normal tothe 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. Practica
31、lly, as long as the geometrical dimensions of the testspecimen are large with respect 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 d
32、irection of displacement isin the major plane of the test specimen.3.2.6 isotropic, adjthe 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
33、and there is a randomdistribution and orientation of phases, crystallites, components, 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
34、 at 0.224 L from each end, where L is the length of thespecimen.3.2.8 out-of-plane flexure, 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 frequen
35、cies of a body driven into flexural, torsional, or longitudinal vibrationthat are determined 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 el
36、astic property testing, a specimen whose ratio of length to minimum cross-sectionaldimension 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 plan
37、e twists around the length dimension axis.4. Summary of Test Method4.1 This test method 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, co
38、ntact accelerometer ornon-contacting microphone) senses the resulting mechanical vibrations 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 sign
39、als are analyzed, and the fundamental resonant frequency is isolated and measured by 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 m
40、ass of the specimen are used to calculate dynamic Youngsmodulus, 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 appr
41、opriate for determining the modulus of advanced ceramics that are elastic,homogeneous, 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 als
42、o be measured similarly, but the required equations fordetermining the moduli are not addressed herein.5.4 This dynamic test method has several advantages and differences from static loading techniques and from resonanttechniques requiring continuous excitation.3 The boldface numbers in parentheses
43、refer to the list of references at the end of this test method.C1259 1435.4.1 The test method is nondestructive in nature and can be used for specimens prepared for other tests. The specimens aresubjected to minute strains; hence, the moduli are measured at or near the origin of the stress-strain cu
44、rve, 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 that require elaborate setup or alignment.5.5 This technique can be used to measure resonant frequencies al
45、one for the purposes of quality control and acceptance of testspecimens of both regular 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,
46、inhomogeneities, porosity, etc) will change the resonant frequency for that specimen. 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
47、known to include the resonant frequency that the specimen must possess if itsgeometry 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
48、 not be suitable for testing byother procedures. This is similar to the evaluation method 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 t
49、hermal history, environment exposure, etc. Specimen descriptions shouldinclude any specific 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 an
