Material properties wave velocities

Shock-compression science originated during and after World War II when experimental facilities for creating planar shock waves were developed, along with prompt instrumentation techniques enabling shock velocity and particle velocity measurements to be made. The main thrust of shock-compression science is to understand the physics and to measure the material properties which govern the outcome of shock-compression events. Experiments involving planar shock waves are the most useful in shock-compression science. 

An exothermic chemical reaction that propagates with such rapidity that the rate of advance of the reaction zone into the unreacted material exceeds the velocity of sound in the unreacted material, that is the advancing reaction zone is preceded by a shock wave. The rate of advance of the reaction zone is termed detonation rate or detonation velocity. When this rate of advance attains such a value that it will continue without diminution thru the unreacted material, it is termed a stable detonation velocity. The exact value of this term is dependent upon a number of factors, principally the chemical and physical properties of the material. When the detonation rate is equal to or greater than the stable detona-... 

Many materials whose elastic properties are of interest are anisotropic, so the surface wave velocity depends on the direction of propagation. In order to be able to make measurements in one direction at a time, a lens with a cylindrical... 

Analysis of these effects is difficult and time consuming. Much recent work has utilized two-dimensional, finite-difference computer codes which require as input extensive material properties, e.g., yield and failure criteria, and constitutive laws. These codes solve the equations of motion for boundary conditions corresponding to given impact geometry and velocities. They have been widely and successfully used to predict the response of metals to high rate impact (2), but extension of this technique to polymeric materials has not been totally successful, partly because of the necessity to incorporate rate effects into the material properties. In this work we examined the strain rate and temperature sensitivity of the yield and fracture behavior of a series of rubber-modified acrylic materials. These materials have commercial and military importance for impact protection since as much as a twofold improvement in high rate impact resistance can be achieved with the proper rubber content. The objective of the study was to develop rate-sensitive yield and failure criteria in a form which could be incorporated into the computer codes. Other material properties (such as the influence of a hydrostatic pressure component on yield and failure and the relaxation spectra necessary to define viscoelastic wave propagation) are necssary before the material description is complete, but these areas will be left for later papers. 

L is the electrode spacing, the wave velocity and k the wave vector, each of which are given by the experimental configuration. A and B are attenuation coefficients and is the potential at the crystal surface, and these three parameters can also be calculated from the geometry and the material properties. The drift mobihty is measured in this experiment and is defined by... 

The attenuation and velocity of acoustic energy in polymers are very different from those in other materials due to their unique viscoelastic properties. The use of ultrasonic techniques, such as acoustic spectroscopy, for the characterization of polymers has been demonstrated [47,48]. For AW devices, the propagation of an acoustic wave in a substrate causes an oscillating displacement of particles on the substrate surface. For a medium in intimate contact with the substrate, the horizontal component of this motion produces a shearing force. In such cases, there can be sufficient interaction between the acoustic wave and the adjacent medium to perturb the properties of the wave. For polymeric materials, attenuation and velocity of the acoustic wave will be affected by changes in the viscoelastic behavior of the polymer. 

Shen AH, Reichmann H-J, Chen G, Angel RJ, Bassett WA, Spetzler H (1998) GHz ultrasonic interferometry in a diamond anvil cell P-wave velocities in periclase to 4.4 GPa and 207°C. In Manghanni MH, Yagi T (eds) Properties of Earth and Planetary Materials at High Pressure and Temperature. Am Geophys Union, Washington, DC, p 71-77... 

Material Constants, Elastic wave velocities have been obtained for oil shale by ultrasonic methods for various modes of propagation. Elastic constants can be inferred from these data if the oil shale is assumed to be a transversely isotropic solid (9). This is a reasonable approximation considering the bedded nature of the rock. Many of the properties of oil shale depend on the grade (kerogen content), which in turn is correlated with the density ( 10). The high pressure behavior of oil shale under shock loading has been studied in gas-gun impact experiments (11). 

Thus far four composites listed in Table I have been studied. NbTi/Cu is discussed briefly here. From its microstructure and manufacture, a rectangular cross-section bar, it was assumed that this composite has orthorhombic (orthotropic) symmetry in its physical properties. Materials with this symmetry have nine independent elastic constants. While deviations from elastic behavior were small, nine independent elastic constants were verified. Four specimens were prepared (Fig. 16) and 18 ultrasonic wave velocities were determined by propagating differently polarized waves in six directions, (100) and (110). An example cooling run is shown in Fig. 17 for E33, Young s modulus along the filament axis. These data typify the composites studies a wavy, irregular modulus/temperature curve. 

The coated material used on the pipe is usually a viscoelastic layer adhered on the pipe. The internal losses in the coated material are modeled according to the theory of linear viscoelasticity, which is also the model implemented in the software DISPERSE [17] used for the wave structure analysis. The shear velocity and shear attenuation of bitumen are obtained from the result of Simonetti measurement [16] for the software used to predict the attenuation of guided wave. The material properties of the other two coated materials are found from the data bank in the DISPERSE software. The theory of linear viscoelasticity for isotropic and homogenous media is modeled in the frequency domain, which leads to linear equation of motion [18]. Thus... 

The configuration of the detection is illustrated in Fig. 7.1, showing two cases. One is the case of buried pulse (force)/sft), and the other is that of surface pulse, fsft). As published by Pekeris (Pekeris 1955), these two forces result in the completely different displacement fields at point x. In Fig. 7.2, examples of Lamb s solutions due to a buried step-function force, where/sO) = hsft), are given. The depth of the source, D, is 6 cm and the horizontal distance, R, is varied as 3 cm, 6 cm and 9 cm. Here P-wave velocity Vp is assumed as 4000 m/s and Poisson s ratio is 0.2. These material properties actually represent those of concrete. Near the epicenter, only P-wave and S-wave are observed as shown in Fig. 7.2 (a). 

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