Uniaxial elastic wave

Howarth et al. (1989) measured various physical properties (density, porosity, velocities, strength, and rock classification properties) oti sandstones and marbles as weU as the penetration rate for different drilling machines. The authors concluded that statistically significant trends exist between the properties and penetration rates, especially for the elastic wave velocity and penetration rate correlation. Figure 7.24 shows the correlation between the compressional wave velocity and uniaxial strength and the penetration rate for diammid and percussion drilling. 

R.J. Clifton, On the Analysis of Elastic/Visco-Plastic Waves of Finite Uniaxial Strain, in Shock Waves and the Mechanical Properties of Solids (edited by J.J. Burke and V. Weiss), Syracuse University Press, 1971, pp. 73-119. 

Another property that is related to chemical hardness is polarizability (Pearson, 1997). Polarizability, a, has the dimensions of volume polarizability (Brinck, Murray, and Politzer, 1993). It requires that an electron be excited from the valence to the conduction band (i.e., across the band gap) in order to change the symmetry of the wave function(s) from spherical to uniaxial. An approximate expression for the polarizability is a = p (N/A2) where p is a constant, N is the number of participating electrons, and A is the excitation gap (Atkins, 1983). The constant, p = (qh)/(2n 2m) with q = electron charge, m = electron mass, and h = Planck s constant. Then, if N = 1, (1/a) is proportional to A2, and elastic shear stiffness is proportional to (1/a). 

The dilational rheology behavior of polymer monolayers is a very interesting aspect. If a polymer film is viewed as a macroscopy continuum medium, several types of motion are possible [96], As it has been explained by Monroy et al. [59], it is possible to distinguish two main types capillary (or out of plane) and dilational (or in plane) [59,60,97], The first one is a shear deformation, while for the second one there are both a compression - dilatation motion and a shear motion. Since dissipative effects do exist within the film, each of the motions consists of elastic and viscous components. The elastic constant for the capillary motion is the surface tension y, while for the second it is the dilatation elasticity e. The latter modulus depends upon the stress applied to the monolayer. For a uniaxial stress (as it is the case for capillary waves or for compression in a single barrier Langmuir trough) the dilatational modulus is the sum of the compression and shear moduli [98]... 

The agreement between fee bulk modulus deduced from Brillouin scattering measurements and fee ADX results is very good. The determination of fee elastic moduli by ultrasonics was made by fee measurement of surface acoustic wave velocities on thin films [22], The second ultrasonics experiment was made on sintered powder, by measuring fee longitudinal and transverse sound velocity at ambient and under uniaxial compression. From feat, fee bulk modulus and its pressure derivative were deduced, but this result seems to be quite imprecise. The ultrasonics experiment on thin films gives rise to a very small difference in fee bulk modulus (5%), but fee ADX or Brillouin determination should be utilised for preference. 

Figure 5 Uniaxial stress versus volume for an overdriven [111] direction shock simulation in a perfect Lennard Jones crystal. The gray line is the Rayleigh line, or constraint line provided by the volume equation of motion Eq. (16). The black line is the actual path of the simulation. The volume begins the simulation at V/V = 1 and subsequently undergoes elastic oscillations around V/V =0.85. As the amplitude of these oscillations decays with time, the simulation trajectory approaches the Rayleigh line. After the oscillations have decayed away, plastic deformation and further compression occur. During this slower plastic wave, the simulation trajectory closely follows the Rayleigh line, ensuring the correct sequence thermodynamic states are sampled.

We have also measured the surface compression elasticity and viscosity of DTAB-PAMPS mixed surface layers. These two coefficients describe the resistance of the layer to a uniaxial compression in the surface plane. They were measured with a device in which surface waves are excited at a frequency of a few hundred hertz. It was found that as expected, the layers start to exhibit a measurable elasticity at surfactant concentrations much less than with pure surfactant solutions (Figure 5). The elasticity (both real and imaginary parts, r and j respectively) exhibits a maximum around CAC and decreases to zero around CMC. 

The crosslinking of polyurethane resin composed of diisocyanate derived from 4,4 -diisocyanate diphenylmethane and a low-viscosity polyethertriol was also investigated under micro-wave conditions. The reactions were carried out without a catalyst and led to final networks with mechanical properties least equivalent to those prepared under conventional conditions. For example, the average elasticity modulus determined from uniaxial compression with samples (25 mm of height and 12.5 mm of diameter) was equal to 3120 MPa for curing under... 

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