Bulk Modulus and Density Measurements of Small Compressible and Incompressible Samples
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Bulk Modulus and Density Measurements of Small Compressible and Incompressible Samples Jack C. Hay and Barry N. Lucas Fast Forward Devices, LLC 11020 Solway School Road, Suite 113 Knoxville, TN 37931
ABSTRACT A novel system is described for determining physical properties, including bulk modulus and density, of small solid samples. The system consists of a chamber in which the sample weight is measured by a weighing device immersed in a gas of controllable density. Thus, the method of measuring density is based on Archimedes’ principle where the weight of an object is reduced by the weight of the displaced fluid. This particular device has been designed for examining the density of disk-shaped samples 3 mm in diameter and 0.4 mm thick. The weighing device has a repeatability of 4 nN and sample densities can be determined to 0.5%. A significant feature of this device is the ability to measure buoyancy forces at a plurality of gas densities, which allows one to capture nonlinear behaviors associated with closed-cell compressible media. Results are presented for a quasi-closed cell foam that experiences volume reduction as the gas pressure is increased. Volumetric strains are determined as the difference between the observed behavior and the linear behavior of incompressible media. Plots of hydrostatic stress versus volumetric strain are initially linear, as described by the bulk modulus, and exhibit a “kink” at high pressures, presumably due to the complete compression of internal cells. BACKGROUND The density of a substance is expressed as a ratio of mass, m, to volume, V, or m/V. This is a physical property of a material that relates to composition, level of impurities, and mixtures, and can be an indicator of hidden features such as voids. In the special case of compressible media, such as closed-pore elastomers, the bulk density is a function of hydrostatic pressure since the volume changes with pressure while the mass remains unchanged. There exist two popular methods for determining the density of a solid: (1) by comparison of the sample density with the densities of substances of known value, usually by hydrostatic weighing in two different fluids of known and substantially differing density (Archimedes principle), and (2) by the independent measurement of mass and volume of the sample. The experimental procedures described here are based on Archimedes principle where the weight of the sample is measured as a function of fluid density. In using this method the measured weight is reduced from the “true” weight (mg) due to the buoyancy forces acting on the object. The sensitivity of the method ultimately relies on the range of available liquid densities and how well one can measure weight. In one typical application of the method, one measures the apparent weight of the object in alcohol and then in water. It is also common practice to weigh the object in air and then in a liquid such as water or alcohol, thus using air as FF3.8.1
the first medium. In that case it is often assumed that the measured weight in a
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