Nuclear Engineering ETDs

Publication Date

5-21-1971

Abstract

Hooke's Law, Newton's Law, and the Grüneisen Equation of State are combined to develop a non-homogeneous, displacement wave equation and the stress/displacement relationship for an isotropic solid in which there has been a time and spatially dependent change in thermal energy. These equations are applied to two solids that are in perfect mechanical contact. One of the materials has had its thermal energy changed along one direction by a high energy electron beam while the thermal energy of the other has remained unchanged. It was assumed that the time dependence of the thermal energy change could be approximated by a ramp function of duration t0. This assumption permitted the displacement wave equation and the stress/displacement relationship to be solved by Laplace transform methods to obtain σmax, the maximum stress in compression normal to the interface of the two materials. This relationship was found to be

σmax = ρ1ϒ1( ) ,

where the 1 subscript refers to the irradiated material and ϒ, ρ, c, and e(x) are the Grüneisen coefficient, density, longitudinal elastic wave velocity, and the change in thermal energy per unit mass, respectively. Under the conditions of the analysis, it was shown that (1) σmax occurred at the time L/c1, where L is the thickness of the irradiated sample and (2) the interface stress went to zero at the time L/c1 + t0/2.In the experiment, one inch diameter by 0.10 inch-thick material samples were bonded to quartz stress gages and irradiated with the 2 MeV pulsed electron beam from the Febetron 705. The material samples were machined from tantalum, furnace-cooled depleted uranium, furnace-cooled depleted uranium alloyed with 1.5 weight percent molybdenum, furnace-cooled depleted uranium alloyed with 10 weight percent molybdenum, and gamma-stabilized depleted uranium alloyed with 10 weight percent molybdenum. The time-dependent quartz gage data provided a measure of σmax, c1, and t0. e(x) was determined from calorimeter measurements of the temperature change through the irradiated specimens. It was observed that t0 increased with the atomic number and density of the irradiated specimens. The Grüneisen coefficients of the test specimens were then computed from these measurements. It was found that (1) they were within experimental measurement error of Grüneisen coefficients computed from other thermodynamic and elastic parameters and (2) the ϒ-phase uranium structures had lower Grüneisen coefficients than the α-phase structures.

Sponsors

The United States Atomic Energy Commission

Document Type

Dissertation

Language

English

Degree Name

Nuclear Engineering

Level of Degree

Doctoral

Department Name

Nuclear Engineering

First Committee Member (Chair)

Lawrence Dare Posey

Second Committee Member

James Albert Horak

Third Committee Member

Jon A. Reuscher

Fourth Committee Member

James Johnson

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