Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio for Advanced Ceramics by Impulse Excitation of Vibration
A non-destructive sonic method is used to determine the modulus of elasticity and modulus of rigidity for calculation of Poisson's Ratio. Bars of rectangular cross-section are used for the measurements.
SIGNIFICANCE AND USE
This test method may be used for material development, characterization, design data generation, and quality control purposes.
This test method is specifically appropriate for determining the modulus of advanced ceramics that are elastic, homogeneous, and isotropic (1).
This test method addresses the room temperature determination of dynamic moduli of elasticity of slender bars (rectangular cross-section) and rods (cylindrical). Flat plates and disks may also be measured similarly, but the required equations for determining the moduli are not addressed herein.
This dynamic test method has several advantages and differences from static loading techniques and from resonant techniques requiring continuous excitation.
The test method is nondestructive in nature and can be used for specimens prepared for other tests. 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.
The impulse excitation test uses an impact tool and simple supports for the test specimen. There is no requirement for complex support systems that require elaborate setup or alignment.
This technique can be used to measure resonant frequencies alone for the purposes of quality control and acceptance of test specimens of both regular and complex shapes. A range of acceptable resonant frequencies is determined for a specimen with a particular 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. Any specimen with a resonant frequency falling outside the prescribed frequency range is rejected. The actual modulus of each specimen need not be determined as long as the limits of the selected frequency range are known to include the resonant frequency that the specimen must possess if its geometry and mass and internal structure are within specified tolerances. The technique is particularly suitable for testing specimens with complex geometries (other than parallelepipeds, cylinders/rods, or discs) that would not be suitable for testing by other procedures. This is similar to the evaluation method described in Guide E 2001.
If a thermal treatment or an environmental exposure affects the elastic response of the test specimen, this test method may be suitable for the determination of specific effects of thermal history, environment exposure, etc. Specimen descriptions should include any specific thermal treatments or environmental exposures that the specimens have received.
1.1 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 dynamic 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 can be measured. Dynamic Young's modulus is determined using the resonant frequency in the flexural mode of vibration. The dynamic shear modulus, or modulus of rigidity, is found using torsional resonant vibrations. Dynamic Young's modulus and dynamic shear modulus are used to compute Poisson's ratio.
1.2 This test method measures the fundamental resonant frequency of test specimens of suitable geometry by exciting them mechanically by a singular elastic strike with an impulse tool. Specimen supports, impulse locations, and signal pick-up points are selected to induce and measure specific modes of the transient vibrations. A transducer (for example, contact accelerometer or non-contacting 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 signal analyzer, which provides a numerical reading that is (or is proportional to) either the frequency or the period of the specimen vibration. The appropriate fundamental resonant frequencies, dimensions, and mass of the specimen are used to calculate dynamic Young's modulus, dynamic shear modulus, and Poisson's ratio.
1.3 Although not specifically described herein, this test method can also be performed at cryogenic and high temperatures with suitable equipment modifications and appropriate modifications to the calculations to compensate for thermal expansion, in accordance 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 Methods C 623, C 747, C 848, and C 1198.
1.5 This test method uses test specimens in bar, rod, and disc geometries. The rod and bar geometries are described in the main body. The disc geometry is addressed in Annex A1.
1.6 A modification of this test method can be used for quality control and nondestructive evaluation, using changes in resonant frequency to detect variations in specimen geometry and mass and internal flaws in 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 responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
FIG. 1 Block Diagram of Typical Test Apparatus
Extracted, with permission, from ASTM C1259 Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio for Advanced Ceramics by Impulse Excitation of Vibration, copyright ASTM International, 100 Barr Harbor Drive, West Conshohocken, PA 19428. A copy of the standard may be purchased from ASTM International, phone 610-832-9555, e-mail: firstname.lastname@example.org, website:www.astm.org.
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