Bulk Modulus Of Particles Research Articles

The debonding toughness in layered particulate polymer composites

Abstract The effect of delamination or cavitation of particles on the toughness of spherical and layered particulate composites is discussed using the Mori–Tanaka model. Both spherical and spheroidal particles are considered. The model is compared with other models reported in literature and shows fair agreement. In general, at the onset of delamination both stress and bulk modulus drop and this drop continues until delamination is complete. The debonding toughness increases with volume fraction but more effectively with particle aspect ratio. Rather surprising is the fact that the debonding toughness does not increase for high ratios of particle bulk modulus to matrix bulk modulus (>20). This may be a consequence of the sharp decrease in the composite bulk modulus as delamination progresses. The study shows marginal increase in toughness especially from debonding of spherical particles.

Numerical Simulation of the Compression Behavior of Nanometer-Sized Ag Particles

The mechanical response to hydrostatic compression of Ag particles in the size range between 1 and 7 nm has been investigated by molecular dynamics simulations. The solid particles were prepared starting from molten droplets cooled at realistic rates and embedded in a pressure-transmitting liquid medium. It is shown that the particle bulk modulus undergoes a size-dependent increase related to the size-dependent variation of the Einstein temperature. This correlates in turn with the fraction of atoms with compact coordination and connects the stiffening of Ag particles with their structure.

Dynamic measurement of sediment grain compressibility at atmospheric pressure: acoustic applications

Under certain conditions, Wood's equation can be used to predict sound speed in fluid/solid-grain suspensions if the bulk moduli and densities of the grains and fluid are known. In this paper, that relationship is used to estimate grain-bulk moduli in suspensions where sound speed, fluid density, fluid bulk modulus, grain density, and particle concentrations are known or accurately measured. Measured values of grain-bulk moduli for polystyrene beads suspended in water (mean = 4.15 /spl times/ 10/sup 9/ Pa) and soda-lime glass beads suspended in a heavy liquid (mean = 3.8 /spl times/ 10/sup 10/ Pa) are consistent with the values of bulk moduli for polystyrene beads and soda-lime glass beads found in the literature (3.6 to 4.2 /spl times/ 10/sup 9/ Pa and 3.4 to 4.0 /spl times/ 10/sup 10/ Pa, respectively). These measurements thus provide controls, which demonstrate the validity of the suspension technique to estimate values of particle bulk modulus. The values of bulk modulus, measured using the same suspension techniques, for Ottawa sand and quartz sand grains collected from the coastal sediments of the northeast Gulf of Mexico ranged between 3.8 and 4.7 /spl times/ 10/sup 10/ Pa, with 95% confidence limits between 3.0-5.7 /spl times/ 10/sup 10/ Pa. These measured values of bulk modulus are consistent with the range of handbook values for polycrystalline quartz (3.6 to 4.0 /spl times/ 10/sup 10/ Pa). The use of the lower bulk modulus (i.e., 7.0 /spl times/ 10/sup 9/ Pa) recently suggested by Chotiros is therefore inappropriate and traditional handbook values of sediment grain-bulk moduli should be used as inputs for sediment acoustic modeling.

Modeling viscoelastic response of particulate polymeric composites with high volume fractions of fillers

A generalized self-consistent method is extended to particulate viscoelastic composites with elastomeric matrices and high volume fractions of elastic inclusions. It is shown that the effective bulk modulus of a composite coincides with the bulk modulus of particles. A quadratic operator equation is derived for an analog of the effective shear relaxation kernel. This equation is explicitly solved using the Laplace transform method. The influence of material and geometrical parameters of a composite on its effective viscoelastic moduli is analyzed numerically.

The effects of particle bulk modulus on toughening mechanisms in rubber‐modified polymers

AbstractThe interaction of a blunting mode I plane‐strain crack tip with a periodic array of initially spherical rubber particles directly ahead of and parallel to the crack front in the effective medium is studied by the crack tip‐particle interaction model. The local stress concentrations responsible for rubber cavitation, matrix crazing and shear yielding are obtained by three‐dimensional large deformation elastic‐plastic finite element analysis with a sub‐modeling technique to explore the relationship between these toughening mechanisms. It is shown that rubber particles can act as stress concentrators to initiate matrix crazing or shear yielding but they behave differently from voids at high triaxiality because of their high bulk modulus. Particle bulk modulus affects significantly the hydrostatic stress inside rubber particles as well as the plastic deformation in the ligament between the crack tip and particles. Rubber cavitation or interface debonding relieves the triaxial stress planestrain condition so that extensive plastic deformation can be developed in the toughening process.

Acoustic properties of ultrasonic contrast agents

Abstract Diameters of particles used as ultrasound contrast agents are limited by capillary diameters to about 8 μm, much smaller than the acoustic wavelength used in diagnostic ultrasound. Strong acoustic backscatter from such small particles is achieved by using gas-containing particles encapsulated in a shell. The shell makes the acoustic properties of these particles differ from that of gas-bubbles. It is shown how acoustic behaviour of such particles can be explained from their size and compressibility. The particle bulk modulus K was described with the Kelvin-Voigt model for visco-elastic solids, K = K0 + iωμ, where the parameters K0 and μ were found from acoustic attenuation spectra. Application of this model to an experimental contrast agent from Nycomed Imaging gave as a result K0 = 2.2 MPa, μ = 0.080 Pa · s.