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Film thickness for different regimes of fluid-film lubrication

Film thickness equations are provided for four fluid-film lubrication regimes found in elliptical contacts. These regimes are isoviscous-rigid; viscous-rigid; elastohydrodynamic lubrication of low-elastic-modulus materials (soft EHL), or isoviscous-elastic; and elastohydrodynamic lubrication of high-elastic-modulus materials (hard EHL), or viscous-elastic. The influence or lack of influence of elastic and viscous effects is the factor that distinguishes these regimes. The results are presented as a map of the lubrication regimes, with film thickness contours on a log-log grid of the viscosity and elasticity for three values of the ellipticity parameter.

Hamrock, B. J.↗

Experimental Identification and Simulation of Time and/or Rate Dependent Reversible and Irreversible Deformation Regions for both a Titanium and Nickel Alloy

In this paper time and/or rate dependent deformation regions are experimentally mapped out as a function of temperature. It is clearly demonstrated that the concept of a threshold stress (a stress that delineate reversible and irreversible behavior) is valid and necessary at elevated temperatures and corresponds to the classical yield stress at lower temperatures. Also the infinitely slow modulus, (Es) i.e. the elastic modulus of the material if it was loaded at an infinitely slow strain rate, and the "dynamic modulus", modulus, Ed, which represents the modulus of the material if it is loaded at an infinitely fast rate are used to delineate rate dependent from rate independent regions. As demonstrated at elevated temperatures there is a significant difference between the two modulus values, thus indicating both significant time-dependence and rate dependence. In the case of the nickel-based super alloy, ME3, this behavior is also shown to be grain size specific. Consequently, at higher temperatures viscoelastic behavior exist below k (i.e., the threshold stress) and at stresses above k the behavior is viscoplastic. Finally a multi-mechanism, stress partitioned viscoelastic model, capable of being consistently coupled to a viscoplastic model is characterized over the full temperature range investigated for Ti-6-4 and ME3.

Arnold, Steven M.↗

Minimum film thickness in elliptical contacts for different regimes of fluid-film lubrication

The film-parameter equations are provided for four fluid-film lubrication regimes found in elliptical contacts. These regimes are isoviscous-rigid; viscous-rigid; elastohydrodynamic of low-elastic-modulus materials, or isoviscous-elastic; and elastohydrodynamic, or viscous-elastic. The influence or lack of influence of elastic and viscous effects is the factor that distinguishes these regimes. The film-parameter equations for the respective regimes come from earlier theoretical studies by the authors on elastohydrodynamic and hydrodynamic lubrication of elliptical conjunctions. These equations are restated and the results are presented as a map of the lubrication regimes, with film-thickness contours on a log-log grid of the viscosity and elasticity parameters for five values of the ellipticity parameter. The results present a complete theoretical film-parameter solution for elliptical contacts in the four lubrication regimes.

Hamrock, B. J.↗

The Influence of Redox Conditions on the Seismic Properties of Polycrystalline Olivine

Eight olivine specimens were fabricated by use of a solgel method and hot-pressing at 1200 degrees Centigrade and 300 megapascals (MPa) inside of welded Pt capsules. Each hot-pressed specimen was then recovered, precision ground, and wrapped in Pt, Ni or NiFe foil to vary oxygen fugacity (fO2) during the subsequent forced torsional oscillation measurements. Mechanical testing was conducted at 10 oscillation periods between 1 and 1000 seconds, at a confining pressure of 200 MPa, during a slow staged-cooling from a maximum temperature of 1200 degrees Centigrade down to room temperature. After mechanical testing, each specimen was axially sectioned and EBSD (Electron BackScatter Diffraction) was used for the determination of the representative grain size, and grain size distribution of each sample. In addition, each longitudinal section was mapped via FTIR (Fourier Transform Infrared Spectroscopy) to determine the spatial distribution and concentrations of chemically bound and molecular water. Amongst these eight specimens, chemically bound ‘water’ contents were observed to vary between 0 and 1150 atom parts per million (ppm) H/Si, and molecular water concentrations varied between 0 and 245 atom ppm H/Si. Our forced-oscillation results demonstrate that the measured magnitude of anelastic relaxation within the experimental ‘window’ of oscillation periods is unrelated to the water content. Rather, a relationship was observed between the magnitude of anelastic relaxation and the prevailing redox conditions, which is influenced by the choice of metal sleeving used during the mechanical test. Further, regardless of water content or metal sleeving, each specimen exhibits coupled variations in shear modulus and dissipation within the observational window, indicative of ‘high-temperature background’ behavior, that can be described by a Burgers-type model. During initial fitting of the Burgers models, the unrelaxed shear modulus at a reference temperature of 900°C (elastic unloading/reloading shear modulus G (sub UR)) and the temperature derivative of the unrelaxed shear modulus (dGU/dT), were treated as adjustable parameters. For all Fe-bearing olivine samples we observe deficits of G (sub UR) and increased values of dGU/dT, relative to the expected elastic (anharmonic) behavior for Fo (Forsterite content percentage) (sub 90) olivine. This behavior is indicative of anelastic relaxation occurring at shorter periods than observable within the ‘window’ of oscillation periods used in the mechanical test. Moving towards a comprehensive and seismologically applicable Burgers model, which includes this newly observed effect of redox conditions on anelastic relaxation, we will present our progress on reconciling truly anharmonic and elastic behavior of Fo (sub 90) olivine with our observed forced-oscillation data.

Cline, C. J., II↗

Quantifying the Influence of Redox Conditions on the Seismic Properties of Olivine

A series of eight olivine specimens were fabricated by hot-pressing at 1200 degrees Celsius and 300 megapascals (MPa). Each hot-pressed specimen was then wrapped in Pt, Ni or NiFe foil to vary oxygen fugacity (fO2), and interrogated via forced torsional oscillation. Mechanical testing was conducted at 10 oscillation periods between 1 and 1000 seconds, at a confining pressure of 200 MPa, during a slow staged-cooling from a maximum temperature of 1200 degrees Celsius to room temperature. After mechanical testing, each specimen was axially sectioned and EBSD (Electron BackScatter Diffraction) was used for the determination of the representative grain size, and grain size distribution of each sample. In addition, each longitudinal section was mapped via FTIR (Fourier Transform InfraRed spectroscopy) to determine the spatial distribution and concentrations of chemically bound and molecular water. Amongst these specimens, chemically bound ‘water’ contents were observed to vary between 0 and 1150 atom ppm (parts per million) H/Si, and molecular water concentrations varied between 0 and 245 atom ppm H/Si. Our forced-oscillation results demonstrate that the measured magnitude of anelastic relaxation within the experimental ‘window’ of oscillation periods is unrelated to the water content. Rather, a relationship was observed between the magnitude of anelastic relaxation and the prevailing redox conditions, which is influenced by the choice of metal sleeving used during the mechanical test. Further, regardless of water content or metal sleeving, each specimen exhibits coupled variations in shear modulus and dissipation within the observational window, indicative of ‘high-temperature background’ behavior, that can be described by a Burgers-type model. During initial fitting of the Burgers models, the unrelaxed shear modulus at a reference temperature of 900 degrees Celsius (G (sub UR)) and the temperature derivative of the unrelaxed shear modulus (dG (sub U)/dT), were treated as adjustable parameters. For all Fe-bearing olivine samples (but not a hydrous and oxidized Fe-free sample) we observe deficits of G (sub UR), and increased values of dG (sub U)/dT, relative to the expected elastic (anharmonic) behavior of Fo90 olivine. This behavior is indicative of anelastic relaxation occurring at shorter periods than observable within the ‘window’ of oscillation periods used in the mechanical test. Moving towards a comprehensive seismologically applicable Burgers model, which includes this newly observed effect of redox conditions on anelastic relaxation, we will present our progress in reconciling truly anharmonic and elastic behavior of Fo (sub 90) olivine with our observed forced-oscillation data.

Cline, Christopher, II↗