ASTM E1876 PDF

Product Details 1. 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 geometry, mass, and mechanical resonant frequencies of a suitable rectangular or cylindrical geometry test specimen of that material can be measured. The dynamic shear modulus, or modulus of rigidity, is found using torsional resonant vibrations.

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A number in parentheses indicates the year of last reapproval. Specimens of these materials possess specific mechanicalresonant 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 or cylindrical geometry test specimen of that material can be measured.

Thedynamic shear modulus, or modulus of rigidity, is found usingtorsional resonant vibrations. Test Methods C, C, C, C,C, and C may differ from this test method in severalareas for example; sample size, dimensional tolerances,sample preparation. The testing of these materials shall bedone in compliance with these material specific standards.

Where possible, the procedures, sample specifications andcalculations are consistent with these test methods. No other units of measurement are included in thisstandard. 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. Referenced Documents2.

Current edition approved April 1, Published April Originallyapproved in Last previous edition approved in as E — United States Also called modulus of rigidity or torsionalmodulus. For the fundamental flexureresonance, the antinodes are located at the two ends and thecenter of the specimen. Most elasticmaterials conform to this definition well enough to make thisresonance test valid.

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. Materials are considered isotropic on a mac-roscopic scale, if they are homogeneous and there is a randomdistribution and orientation of phases, crystallites, components,pores, or microcracks.

Forthe fundamental flexural resonance of such a rod or bar, thenodes are located at 0. The lowest resonant frequency in agiven vibrational mode is the fundamental resonant frequencyof that mode. Summary of Test Method4. A transducer for example, 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 signals 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. Significance and Use5. Flat platesand disks may also be measured similarly, but the requiredequations for determining the moduli are not addressed herein. 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.

There is no requirementfor complex support systems that require elaborate setup oralignment. A range ofacceptable resonant frequencies is determined for a specimenwith a particular geometry and mass.

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 frequency range are known to include the resonantfrequency that the specimen must possess if its geometry andmass are within specified tolerances.

Speci-men descriptions should include any specific thermal treat-ments or environmental exposures that the specimens havereceived. The character volume fraction, size, morphology, distribution,orientation, elastic properties, and interfacial bonding of thereinforcement and inhomogeneities in the specimens will havea direct effect on the elastic properties of the specimen as awhole.

These effects must be considered in interpreting the testresults for composites and inhomogeneous materials. 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.

This test method is not appropriate fordetermining the elastic properties of materials that cannot befabricated into such geometries. Deviations from the specified tolerances for the dimensions ofthe specimens will change the resonant frequencies and intro-duce error into the calculations.

Edge chamfers changethe resonant frequency of the test bars and introduce error intothe calculations of the dynamic modulus. It is recommendedthat specimens for this test method not have chamfered orrounded edges. For example, in the calculation of dynamicmodulus, the modulus value is inversely proportional to thecube of the thickness. Uniform specimen dimensions andprecise measurements are essential for accurate results.

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A number in parentheses indicates the year of last reapproval. Specimens of these materials possess specific mechanicalresonant 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 or cylindrical geometry test specimen of that material can be measured. Thedynamic shear modulus, or modulus of rigidity, is found usingtorsional resonant vibrations. Test Methods C, C, C, C,C, and C may differ from this test method in severalareas for example; sample size, dimensional tolerances,sample preparation. The testing of these materials shall bedone in compliance with these material specific standards. Where possible, the procedures, sample specifications andcalculations are consistent with these test methods.

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ASTM E1876

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 geometry, mass, and mechanical resonant frequencies of a suitable rectangular or cylindrical geometry test specimen of that material can be measured. The dynamic shear modulus, or modulus of rigidity, is found using torsional resonant vibrations. Test Methods C, C, C, C, C, and C may differ from this test method in several areas for example; sample size, dimensional tolerances, sample preparation. The testing of these materials shall be done in compliance with these material specific standards.

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ASTM E1876 - 15

Significance and Use 5. Flat plates may also be measured similarly, but the required equations for determining the moduli are not presented. The specimens are subjected to minute strains; hence, the moduli are measured at or near the origin of the stress-strain curve, with the minimum possibility of fracture. There is no requirement for complex support systems that require elaborate setup or alignment. A range of acceptable resonant frequencies is determined for a specimen with a particular geometry and mass. Any specimen with a frequency response falling outside the prescribed frequency range is rejected.

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