Modulus ultrasonic

Phase Structure Lattice parameter (room temperature) (A) Density (gcm ) Nano- hardness (GPa) Microhardness (100 g load) (GPa) Young s modulus (from nanohardness) (GPa) Yoimg s modulus (Ultrasonic) (GPa)... 

Ultrasonic Microhardness. A new microhardness test using ultrasonic vibrations has been developed and offers some advantages over conventional microhardness tests that rely on physical measurement of the remaining indentation size (6). The ultrasonic method uses the DPH diamond indenter under a constant load of 7.8 N (800 gf) or less. The hardness number is derived from a comparison of the natural frequency of the diamond indenter when free or loaded. Knowledge of the modulus of elasticity of the material under test and a smooth surface finish is required. The technique is fast and direct-reading, making it useful for production testing of similarly shaped parts. 

Fig. 7. Relations between elastic constants and ultrasonic wave velocities, (a) Young s modulus (b) shear modulus (c) Poisson s ratio and (d) bulk...

Acoustic Measurements. Measurement of the propagation of ultrasonic acoustic waves has been found useful for determining the viscoelastic properties of thin films of adhesives. In this method, the specimen is clamped between transmitting and receiving transducers. The change in pulse shape between successive reverberation of the pulse is dependent on the viscoelastic properties of the transmitting material. Modulus values can be calculated (267,268). 

The ultrasonic relaxation loss may involve a thermally activated stmctural relaxation associated with a shifting of bridging oxygen atoms between two equihbrium positions (169). The velocity, O, of ultrasonic waves in an infinite medium is given by the following equation, where M is the appropriate elastic modulus, and density, d, is 2.20 g/cm. ... 

Part AM This part lists permitted individual constnic tion materials, apphcable specifications, special requirements, design stress-intensity vafues, and other property information. Of particular importance are the ultrasonic-test and tou ness requirements. Among the properties for which data are included are thermal conduc tivity and diffusivity, coefficient of theiTnal expansion, modulus of elasticity, and yield strength. The design stress-intensity values include a safety factor of 3 on ultimate strength at temperature or 1.5 on yield strength at temperature. 

L. Sandrin, M. Tanter, S. Catheline and M. Fink, Shear modulus imaging with 2-D transient elastography, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 2002, 49, 426 135. 

Cho, C.R. and Jang, J. (1990). Adhesion of ultrasonic high modulus polyethylene fiber-epoxy composite interfaces. In Controlled Interphases in Composite Materials, Prod. ICCI-III, (H. Ishida ed.), Elsevier Sci. Pub., New York, pp. 97 107. 

What is involved in the calculation of modulus First, we mean by modulus in materials science a relation between stress and strain in a bulk sample under practical conditions. This means in effect a testing rate or frequency usually less than a few kilohertz or at the most in the ultrasonic region of, say, 10 MHz. We also suppose the sample to be a representative volume element of size suitable for the test method and we assume its elastic properties to be uniform over this RVE. 

Here E is the appropriate elastic modulus (which depends on the physical state of the material and the type of wave propagating) and p is the density. By combining equations 3 and 4 the physical properties of a material (E and p) can be related to its ultrasonic properties (c and a). 

Thus a measurement of the ultrasonic properties can provide valuable information about the bulk physical properties of a material. The elastic modulus and density of a material measured in an ultrasonic experiment are generally complex and frequency dependent and may have values which are significantly different from the same quantities measured in a static experiment. For materials where the attenuation is not large (i.e., a ca/c) the difference is negligible and can usually be ignored. This is true for most homogeneous materials encountered in the food industry, e.g., water, oils, solutions. 

The velocity is therefore determined by two fundamental physical properties of a material its elastic modulus and density. The less dense a material or the more resistant it is to deformation the faster an ultrasonic wave propagates. Usually, differences in the moduli of materials are greater than those in density and so the ultrasonic velocity is determined more by the elastic moduli than by the density. This explains why the ultrasonic velocity of solids is greater than that of fluids, even though fluids are less dense [1],... 

Thus a measurement of the ultrasonic velocity and density can be used to determine the adiabatic compressibility (or bulk modulus) of the material. For homogeneous solids measurements of the compression and shear velocities can be used to determine the bulk and shear moduli (see section 2.4). The Young s modulus of rod-like materials (e.g. spaghetti) can be determined by measuring the velocity of ultrasound. 

Ultrasonic waves have frequencies which are beyond human hearing. These wave are able to penetrate matter to some extent and the rest is reflected. The E modulus and the density of the material both determine at which speed the waves move through the material. The intensity of the penetrated or reflected beam is measured. The method is for instance used to track defects/ flaws in the material and to measure the E modulus. 

Ultrasonic spectroscopy has been utilized for real-time measurements of polymerization reactions and polymer melt extrusion.15,16 In these applications the time required for the ultrasonic waves to propagate through the sample to a transducer was measured. The velocity of the sound wave in the medium is related to the modulus and density of the sample matrix. 

The ring-opening metathesis polymerization of dicyclopentadiene was monitored by ultrasonic spectroscopy.16 The thermoset poly(dicyclopentadiene) is formed by ringopening and cross-linking in a reaction injection molding system. A reaction cell with a plastic window was constructed for use with pulse echo ultrasonic spectroscopy. Realtime measurements of density, longitudinal velocity, acoustic modulus and attenuation were monitored. Reaction kinetics were successfully determined and monitored using this technique. 

Table 10.4 Density, hydroxyl concentration, crosslink density, packing density, ultrasonic bulk modulus, average atomic mass (g mol-1, prefactor of Eq. (10.2) calculated from Eq. (10.19), calculated density from Eq. (10.21). Experimental data from Morel et al. (1989). 

Table 11.2 Crosslink density, glass transition temperature, and Young s modulus (Et from tensile test at 10 3, s 1 strain rate, Eu from ultrasonic propagation at 5 MHz frequency) for triglycidyl aminophenol-diaminodyphenylmethane-aniline (TGAP-DDM-AN) networks. (After Morel et a ., 1989.)... 

Morel et al., 1989) (Table 11.2). In this series, the tensile modulus increases 17% when 75% of DDM is replaced by aniline, whereas the ultrasonic modulus decreases slightly ( 6%). 

Since the unrelaxed bulk modulus, Ku e.g., determined by ultrasonic propagation velocity measurements, is a good measure of the cohesive energy density, CED (Ku 11 CED Chapter 10), and CED gives a good indication of the overall material s polarity, one can expect a correlation between Ku and W. This is shown in Fig. 14.3 for the amine-epoxy and styrene-vinyl ester networks. The following relationship is found ... 

Predictions of Woo could be performed using global (Hildebrand) or partial (Hansen) solubility parameters, but these are very difficult (and perhaps impossible) to determine accurately from solvent-sorption experiments, so that this way is not realistic. The best experimental approach is, in our opinion, using the ultrasonic modulus. 

At very high pressures, above 12 GPa, and temperatures above 1000 K, a transparent,yellowish, ultra-hard material, believed to consist of the remnants of collapsed molecules, is formed. In several cases ultrasonic, scratch, and indentation studies have shown this material to have a bulk modulus and hardness far exceeding that of diamond [123,131,147], although these reports are by no means uncontested [124,148,149]. The material is extremely disordered and probably has a high fraction of sp2 coordinated bonds, but the structure is unknown. There are some similarities with amorphous carbon (ta-C),but differences in Raman spectra and mechanical properties show that the structures differ. The question of bond types is interesting, since sp2 bonds are known to be stronger than sp3 ones. The materials are semiconducting and have Debye temperatures near 1450 K, somewhat lower than that of diamond [150]. 

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