Designation: C1259 − 15Standard Test Method forDynamic Young’s Modulus, Shear Modulus, and Poisson’sRatio for Advanced Ceramics by Impulse Excitation ofVibration1This standard is issued under the fixed designation C1259; the number immediately following the designation indicates the year oforiginal 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 dynamicelastic properties 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, mass, and mechanical resonantfrequencies of a suitable (rectangular, cylindrical, or discgeometry) test specimen of that material can be measured.Dynamic Young’s modulus is determined using the resonantfrequency in the flexural mode of vibration. The dynamic shearmodulus, or modulus of rigidity, is found using torsionalresonant vibrations. Dynamic Young’s modulus and dynamicshear modulus are used to compute Poisson’s 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 impulsetool. 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 theminto 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 appropriate funda-mental resonant frequencies, dimensions, and mass of thespecimen are used to calculate dynamic Young’s modulus,dynamic shear modulus, and Poisson’s ratio.1.3 Although not specifically described herein, this testmethod can also be performed at cryogenic and high tempera-tures with suitable equipment modifications and appropriatemodifications to the calculations to compensate for thermalexpansion, in accordance with sections 9.2, 9.3, and 10.4 ofC1198.1.4 Where possible, the procedures, sample specifications,and calculations in this test method are consistent with TestMethods C623, C747, C848, and C1198.1.5 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, 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 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:2C372 Test Method for Linear Thermal Expansion of Porce-lain Enamel and Glaze Frits and Fired Ceramic WhitewareProducts by the Dilatometer MethodC623 Test Method for Young’s Modulus, Shear Modulus,and Poisson’s Ratio for Glass and Glass-Ceramics byResonanceC747 Test Method for Moduli of Elasticity and FundamentalFrequencies of Carbon and Graphite Materials by SonicResonanceC848 Test Method for Young’s Modulus, Shear Modulus,and Poisson’s Ratio For Ceramic Whitewares by Reso-nance1This test method is under the jurisdiction of ASTM Committee C28 onAdvanced Ceramics and is the direct responsibility of Subcommittee C28.01 onMechanical Properties and Performance.Current edition approved Feb. 1, 2015. Published April 2015. Originallyapproved in 1994. Last previous edition approved in 2014 as C1259 – 14. DOI:10.1520/C1259-15.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at

[email protected] For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1C1145 Terminology of Advanced CeramicsC1161 Test Method for Flexural Strength of AdvancedCeramics at Ambient TemperatureC1198 Test Method for Dynamic Young’s Modulus, ShearModulus, and Poisson’s Ratio for Advanced Ceramics bySonic ResonanceD4092 Terminology for Plastics: Dynamic MechanicalPropertiesE6 Terminology Relating to Methods of Mechanical TestingE177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE691 Practice for Conducting an Interlaboratory Study toDetermine the Precision of a Test MethodE2001 Guide for Resonant Ultrasound Spectroscopy forDefect Detection in Both Metallic and Non-metallic Parts3. Terminology3.1 Definitions:3.1.1 The definitions of terms relating to mechanical testingappearing in Terminology E6 should be considered as applyingto the terms used in this test method. The definitions of termsrelating to advanced ceramics appearing inTerminology C1145should be considered as applying to the terms used in this testmethod. Directly pertinent definitions as listed in Terminolo-gies E6, C1145, and D4092 are shown in the followingparagraphs with the appropriate source given in brackets.3.1.2 advanced ceramic, n—a highly engineered, high-performance, predominately nonmetallic, inorganic, ceramicmaterial having specific functional attributes. (C1145)3.1.3 dynamic mechanical measurement, n—a technique inwhich 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. (D4092)3.1.4 elastic limit [FL–2],n—the greatest stress that amaterial is capable of sustaining without permanent strainremaining upon complete release of the stress. (E6)3.1.5 elastic modulus [FL–2] ,n—the ratio of stress to strainbelow the proportional limit. (E6)3.1.6 Poisson’s ratio (µ) [nd],n—the absolute value of theratio of transverse strain to the corresponding axial strainresulting from uniformly distributed axial stress below theproportional limit of the material.3.1.6.1 Discussion—In isotropic materials, Young’s Modu-lus (E), shear modulus (G), and Poisson’s ratio (µ) are relatedby the following equation:µ 5 ~E/2G! 2 1 (1)(E6)3.1.7 proportional limit [FL–2] ,n—the greatest stress that amaterial is capable of sustaining without deviation fromproportionality of stress to strain (Hooke’s law). (E6)3.1.8 shear modulus (G) [FL–2] ,n—the elastic modulus inshear or torsion. Also called modulus of rigidity or torsionalmodulus. (E6)3.1.9 Young’s modulus (E) [FL–2] ,n—the elastic modulus intension or compression. (E6)3.2 Definitions of Terms Specific to This Standard:3.2.1 antinodes, n—two 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, adj—the 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, 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 flexural vibrations, n—the vibrations that occur whenthe displacements in a slender rod or bar are in a plane normalto the length dimension.3.2.4 homogeneous, adj—the condition of a specimen 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 microcracks, the bodycan be considered homogeneous.3.2.5 in-plane flexure, n—for 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, adj—the 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 arandom distribution and orientation of phases, crystallites,components, pores, or microcracks.3.2.7 nodes, n—one or more locations in a slender rod or barin 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, n—for 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, n—naturally occurring frequen-cies of a body driven into flexural, torsional, or longitudinalvibration that are determined by the elastic modulus, mass, andFIG. 1 Block Diagram of Typical Test ApparatusC1259 − 152dimensions of the body. The lowest resonant frequency in agiven vibrational mode is the fundamental resonant frequencyof that mode.3.2.10 slender rod or bar, n—in 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, 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 fundamental resonantfrequency of test specimens of suitable geometry (bar, rod, ordisc) by exciting them mechanically by a singular elastic strikewith an impulse tool. A transducer (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 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 frequencies, dimensions, and mass of thespecimen are used to calculate dynamic Young’s modulus,dynamic shear modulus, and Poisson’s 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 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 platesand 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 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 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 the 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. Deviations in specimendimensions or mass and internal flaws (cracks, delaminations,inhomogeneities, porosity, etc) will change the resonant fre-quency for that specimen. Any specimen 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 and 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 described in Guide E2001.5.6 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 thermal 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 applicableto 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 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 If specific surface treatments (coatings, machining,grinding, etching, etc.) change the elastic properties of the