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Results for “bulk modulus”

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NASA NTRS1973

Elasticity of some mantle crystal structures. II.

The single-crystal elastic constants are determined as a function of pressure and temperature for rutile structure germanium dioxide (GeO2). The data are qualitatively similar to those of rutile TiO2 measured by Manghnani (1969). The compressibility in the c direction is less than one-half that in the a direction, the pressure derivative of the shear constant is negative, and the pressure derivative of the bulk modulus has a relatively high value of about 6.2. According to an elastic strain energy theory, the negative shear modulus derivative implies that the kinetic barrier to diffusion decreases with increasing pressure.

Wang, H.↗

NASA NTRS1973

A shock-induced phase change in orthoclase.

New shock compression data to 340 kb for single-crystal orthoclase (along (001)), demonstrate the onset of a shock-induced phase change at about 115 kb. Along the Hugoniot a mixed-phase region extends to about 300 kb, above which the data are believed to correspond to the properties of a high-pressure phase having the hollandite structure (zero pressure density of 3.84 g/cu cm) reported by Ringwood et al. If the hollandite value for the zero pressure density is used, the zero pressure bulk modulus of this phase is approximately 1.8 plus or minus 0.2 Mb.

Ahrens, T. J.↗

NASA NTRS1973

Elasticity of water-saturated rocks as a function of temperature and pressure.

Compressional and shear wave velocities of water-saturated rocks were measured as a function of both pressure and temperature near the melting point of ice to confining pressure of 2 kb. The pore pressure was kept at about 1 bar before the water froze. The presence of a liquid phase (rather than ice) in microcracks of about 0.3% porosity affected the compressional wave velocity by about 5% and the shear wave velocity by about 10%. The calculated effective bulk modulus of the rocks changes rapidly over a narrow range of temperature near the melting point of ice, but the effective shear modulus changes gradually over a wider range of temperature. This phenomenon, termed elastic anomaly, is attributed to the existence of liquid on the boundary between rock and ice due to local stresses and anomalous melting of ice under pressure.

Takeuchi, S.↗

NASA NTRS1974

Elastic moduli of precompressed pyrophyllite used in ultrahigh pressure research

The propagation of ultrasonic pulses in pyrophyllite specimens was studied to determine the effect of specimen precompression on the measured elastic moduli. Measurements were made at room pressure and, for the precompressed specimens, to pressures of 3 kbar. Pyrophyllite was found to be elastically anisotropic, apparently the result of the fabric present in our material. The room pressure adiabatic bulk modulus as measured on specimens made of isostatically compacted powered pyrophyllite was determined to be 96.1 kbar. The wave speeds of ultrasonic pulses in pyrophyllite were found to decrease with increasing specimen precompression. A limiting value of precompression was found, above which no further decrease in wave speed was observed. For the shear wave speeds this occurs at 10 kbar while for the longitudinal wave at 25 kbar. In the limit, the shear waves propagate 20% slower than in the unprecompressed samples; for the longitudinal wave the difference is 30%.

Sachse, W.↗

NASA NTRS1974

Thermoelastic constitutive equations for chemically hardening materials

Thermoelastic constitutive equations are derived for a material undergoing solidification or hardening as the result of a chemical reaction. The derivation is based upon a two component model whose composition is determined by the degree of hardening, and makes use of strain-energy considerations. Constitutive equations take the form of stress rate-strain rate relations, in which the coefficients are time-dependent functions of the composition. Specific results are developed for the case of a material of constant bulk modulus which undergoes a transition from an initial liquidlike state into an isotropic elastic solid. Potential applications are discussed.

Shaffer, B. W.↗

NASA NTRS1976

Fluid property measurements study

Fluid properties of refrigerant-21 were investigated at temperatures from the freezing point to 423 Kelvin and at pressures to 1.38 x 10 to the 8th power N/sq m (20,000 psia). The fluid properties included were: density, vapor pressure, viscosity, specific heat, thermal conductivity, thermal expansion coefficient, freezing point and bulk modulus. Tables of smooth values are reported.

Devaney, W. E.↗

NASA NTRS1980

Theory of bubble dynamics in condensed explosive during start-up transient

Test firings with experimental liquid propellant gun systems indicate that the main concern standing in the way of practical application of LPG's is the possibility of unexpected explosions during start up when pressure is rapidly applied to the liquid monopropellant in the chamber. The phenomenon of many collapse-rebound cycles of imploding bubbles is theorized as the probable cause of explosions in LP systems. It may be concluded that LPG safety would be enhanced by choosing an LP with low bulk modulus, as well as low decomposition reaction rate, and that a benign looking DTA trace is not a sufficient quarantee of insensitivity to a pressure induced explosion. It is also shown that pre-pressurizing an LP charge, thus pre-compressing the bubbles near-isothermally, makes the system relatively insensitive to such pressure induced explosions. The applicability of this analysis to the question of acceleration induced explosion of explosive filled warheads is indicated.

Benreuven, M.↗

NASA NTRS1980

Anorthite - Thermal equation of state to high pressures

New shock-wave data are presented for anorthite from which a full high-temperature, high-pressure equation of state is derived. Whereas anorthite has relatively low values of thermal expansion and Grueneisen parameter at zero pressure, it is found that these attain relatively high values in the high density state corresponding to the high-pressure phase Hugoniot but decrease upon compression as expected. It is noted that higher order anharmonic contributions decrease more rapidly with pressure and that the thermal expansion therefore saturates to a high temperature value at pressures above about 100 GPa. Reduction of the Hugoniot data permits shock temperatures to be calculated; it also yields a principal adiabat for the high pressure branch of the Hugoniot. The initial bulk modulus of this adiabat is essentially identical to that of anorthite, whereas the initial density is about 3.40 Mg/cu m.

Jeanloz, R.↗

NASA NTRS1982

Use of Froehlich-Raimes and other electronic models for physical properties of metals and alloys

The effectiveness of the Froelich-Raimes model in treating force constants and alloy behavior is discussed. Typical predictions of trends include the deviation of Vegard's Law and the variation of the bulk modulus with pressure and with alloying elements. The simple model of Koskimaki and Waber using the linear combination of the density of states led to several useful predictions for titanium based alloys.

Waber, J. T.↗

NASA NTRS1984

Preliminary investigation of an electrical network model for ultrasonic scattering

The behavior of acoustic attenuation in a solid is related to the electrical transmission line model where the electrical shunt conductance, which is frequency dependent, represents the loss due to the scattering sites in the solid. Results indicate that the absolute value of attenuation at a given frequency depends on both the normalized mean square deviation of the density and bulk modulus of the scattering sites from the ambient medium and the spatial scattering correlation function. Besides establishing the absolute value of attenuation, the spatial correlation function determines the attenuation profile as a function of frequency.

Maisel, J. E.↗

NASA NTRS1985

Adiabatic thermal models for planetary bodies

In a number of recent experiments it was found that the logarithmic derivative with respect to volume of the adiabatic temperature increase with pressure P to be an approximately constant quantity n. It was found that n decreases slightly with temperature, to be virtually unaffected by increasing pressure and to take values between 4 and 8 for a wide variety of materials. It is shown that these findings can be substantiated from thermodynamic arguments, finite strain theory, atomic potential theory and experimental data on the thermal expansion coefficient and the bulk modulus B. It will be shown that n is independent of pressure if it is exactly equal to dB/dP + 1. For these materials d log gamma/d log v = -1, where gamma is the thermodynamic Gruneisenparameter. It will increase with P during an isothermal transformation if n dB/dP + 1 and decrease of n dB/dP + 1. For most materials n is close to dB/dP and the changes will be slight if pressures do not become too extreme. During an adiabatic transformation n is virtually constant. Adiabatic thermal models for planetary bodies were calculated and are presented.

Spohn, T.↗

NASA NTRS1984

Theory of the spin-1 bosonic liquid metal - Equilibrium properties of liquid metallic deuterium

The theory of a two-component quantum fluid comprised of spin-1/2 fermions and nonzero spin bosons is examined. This system is of interest because it embodies a possible quantum liquid metallic phase of highly compressed deuterium. Bose condensation is assumed present and the two cases of nuclear-spin-polarized and -unpolarized systems are considered. A significant feature in the unpolarized case is the presence of a nonmagnetic mode with quadratic dispersion owing its existence to nonzero boson spin. The physical character of this mode is examined in detail within a Bogoliubov approach. The specific heat, bulk modulus, spin susceptibility, and thermal expansion are all determined. Striking contrasts in the specific heats and thermal-expansion coefficients of the liquid and corresponding normal solid metallic phase are predicted.

Oliva, J.↗

NASA NTRS1986

Universality in the compressive behavior of solids

It was discovered that the isothermal equation of state for solids in compression is a simple, universal form. This single form accurately describes the pressure and bulk modulus as a function of volume for tonic, metallic, covalent, and rare gas solids.

Vinet, P.↗

NASA NTRS1986

Computational fluid mechanics utilizing the variational principle of modeling damping seals

A computational fluid dynamics code for application to traditional incompressible flow problems has been developed. The method is actually a slight compressibility approach which takes advantage of the bulk modulus and finite sound speed of all real fluids. The finite element numerical analog uses a dynamic differencing scheme based, in part, on a variational principle for computational fluid dynamics. The code was developed in order to study the feasibility of damping seals for high speed turbomachinery. Preliminary seal analyses have been performed.

Abernathy, J. M.↗

NASA NTRS1987

The stability of a sample in a diamond anvil cell

A theoretical analysis of the stability of a gasketed sample in a diamond anvil cell is reported, demonstrating that the stability of the sample depends principally on the yield strength and the thickness of the gasket, the bulk modulus and the radius of the sample, and the geometry of the culet. The results yield a simple methodology that can be used to obtain stable samples in a diamond anvil cell.

Moss, William C.↗

NASA NTRS1987

Combustion stability analysis of preburners in liquid propellant rocket engines during shutdown

A linearized one-dimensional lumped-parameter model capable of predicting the occurrence of the low frequency combustion instability (chugging) experienced during preburner shutdown in the Space Shuttle Main Engines is discussed, and predictions are compared with NASA experimental results. Results from a parametric study of parameters including chamber pressure, fuel and oxygen temperatures, and the effective bulk modulus of the liquid oxidizer suggest that chugging is probably affected by conditions at shutdown through the fuel and oxidizer temperatures. It is suggested that chugging is initiated when the fuel, oxidizer, and helium temperature and flow rates pass into an unstable region, and that chugging may be terminated by decaying pressures.

Lim, Kair-Chuan↗

NASA NTRS1987

Cell model and elastic moduli of disordered solids - Low temperature limit

The cell theory has been previously employed to compute the equation of state of a disordered condensed system. It is now generalized to include anisotropic stresses. The condition of affine deformation is adopted, transforming an orginally spherical into an ellipsoidal cell. With a Lennard-Jones n-m potential between nonbonded centers, the formal expression for the deformational free energy is derived. It is to be evaluated in the limit of the linear elastic range. Since the bulk modulus in this limit is already known, it is convenient to consider a uniaxial deformation. To begin with, restrictions are made to the low-temperature limit in the absence of entropy contributions. Young's modulus and Poisson's ratio then follow.

Peng, S. T. J.↗

NASA NTRS1987

Compressibility of solids

A universal form is proposed for the equation of state (EOS) of solids. Good agreement is found for a variety of test data. The form of the EOS is used to suggest a method of data analysis, which is applied to materials of geophysical interest. The isothermal bulk modulus is discussed as a function of the volume and of the pressure. The isothermal compression curves for materials of geophysical interest are examined.

Vinet, P.↗