The nonlinear viscoelastic behavior of polypropylene

A series of tensile relaxation tests is performed on isotactic polypropylene in the sub-yield and post-yield regions at room temperature. Constitutive equations are derived for the time-dependent response of a semicrystalline polymer at isothermal loading with small strains. Adjustable parameters in the stress-strain relations are found by fitting experimental data. It is demonstrated that the growth of the longitudinal strain results in an increase in the relaxation rate in a small interval of strains in the sub-yield domain. When the strain exceeds some critical value which is substantially less than the apparent yield strain, the relaxation process becomes strain-independent.Comment: 20 pages, 6 figure

Modelling the linear viscoelastic behavior of silicate glasses near the glass transition point

A model is derived for the viscoelastic response of glasses at isothermal uniaxial deformation with small strains. A glass is treated as an ensemble of relaxing units with various activation energies for rearrangement. With reference to the energy-landscape concept, the rearrangement process is thought of as a series of hops of relaxing units (trapped in their potential wells on the energy landscape) to higher energy levels. Stress-strain relations are developed by using the laws of thermodynamics. Adjustable parameters are found by fitting experimental data in torsional dynamic tests on a multicomponent silicate glass at several temperatures near the glass transition point.Comment: 17 pages, 17 figure

The effect of strain rate on the viscoplastic behavior of isotactic polypropylene at finite strains

Two series of uniaxial tensile tests are performed on isotactic polypropylene with the strain rates ranging from 5 to 200 mm/min. In the first series, injection-molded specimens are used without thermal pre-treatment, whereas in the other series, the samples are annealed for 51 h at 160C prior to testing. A constitutive model is developed for the viscoplastic behavior of isotactic polypropylene at finite strains. A semicrystalline polymer is treated as an equivalent heterogeneous network of chains bridged by permanent junctions (physical cross-links and entanglements). The network is thought of as an ensemble of meso-regions connected with each other by links (lamellar blocks). In the sub-yield region of deformations, junctions between chains in meso-domains slide with respect to their reference positions (which reflects sliding of nodes in the amorphous phase and fine slip of lamellar blocks). Above the yield point, sliding of nodes is accompanied by displacements of meso-domains in the ensemble with respect to each other (which reflects coarse slip and fragmentation of lamellar blocks). Stress-strain relations for a semicrystalline polymer are derived by using the laws of thermodynamics. The constitutive equations are determined by 5 adjustable parameters that are found by matching observations. Fair agreement is demonstrated between the experimental data and the results of numerical simulation.Comment: 27 pages, 20 figure

Bahrain - Managing a nonrenewable resource : savings and exchange-rate policies

Bahrain's oil-producing economy is vulnerable to terms-of-trade shocks for oil in the short to medium run. But the country's dependence on nonrenewable hydrocarbon resources represents a more basic constraint on Bahrain's prospects for long-term economic growth and welfare. To maintain economic growth and welfare in the post-oil era, Bahrain must save more of its oil revenues and assets and use them to invest abroad and to support economic diversification. The authors derive optimum domestic savings rates for Bahrain in the context of a two-assets (oil and non-oil) intertemporal welfare-maximizing model. Based on these derived rates, they recommend that the current suboptimal savings ratios be raised by about 10 percent of GDP. Achieving such a high savings rate is probably not economically feasible or politically sustainable in a stagnant economy, because it implies significantly reducing absolute levels of real consumption. Such austerity would not be necessary in a growing, efficiently restructured, and diversified economy, in which the real exchange rate policy played a key role by stimulating non-oil tradable sectors that could replace oil when it dries out. But the success of real exchange rate depreciation itself depends on a sufficiently high savings rate, to free up resources to switch to the production of other tradables. The authors present an empirical three-sector model of the real exchange rate, which permits links between the equilibrium real exchange rate and the optimum savings rate. They use this model to compute what real depreciation is required consistent with the derived optimum savings ratios. Their model predicts that a real depreciation of about 31 percent would be needed between 1992 and 2005 to avert serious overvaluation over this period.Macroeconomic Management,Environmental Economics&Policies,Economic Theory&Research,Banks&Banking Reform,Economic Stabilization

Labor and women's nutrition : a study of energy expenditure, fertility, and nutritional status in Ghana

Economic approaches to health and nutrition have focused largely on measures of child nutrition and related variables (such as birth weight) as indicators of household production of nutritional outcomes. But when dealing with adult nutrition, economists have to address an issue that has generated tremendous controversy in the clinical nutrition literature. That issue is heterogeneity in an individual's energy expenditures. Preschoolers'energy expenditure also differs, but the differences are small enough to be ignored. Not so for adults, whose waking hours are devoted mostly to labor activities of which the energy costs vary enormously. Variables measuring time allocation to various types of labor tasks were used to proxy differences in energy expenditure. Parity has also been hypothesized to be an important determinant of female nutritional health in high fertility countries - with rapid reproductive cycling contributing to a cumulative nutritional decline. But the"maternal depletion syndrome"remains controversial. Much of the evidence to date has been impressionistic - or the results of studies based on small, nonrandom cohorts. Higgins and Alderman used a two-step instrumental variables technique to get consistent estimates of the structural parameters. Energy expenditure, as embodied in individual time allocations over the previous seven days, was found to be an important determinant of women's nutritional status. Time devoted to agricultural tasks, in particular, had a strong negative effect. The results also appear to confirm the existence of a maternal depletion syndrome. Perhaps more important, evidence was found of a substantial downward bias of the calorie-elasticity estimate when the energy expenditure proxies were excluded.Health Monitoring&Evaluation,Health Economics&Finance,Agricultural Knowledge&Information Systems,Environmental Economics&Policies,Economic Theory&Research

Three dimensional finite element ablative thermal response analysis applied to heatshield penetration design

Heatshield design and analysis has traditionally been a decoupled process, the designer creates the geometry generally without knowledge about how the design variables affect the thermostructural response or how the system will perform under off nominal conditions. Heatshield thermal and structural response analyses are generally performed as separate tasks where the analysts size their respective components and feedback their results to the designer who is left to interpret them. The analysts are generally unable to provide guidance in terms of how the design variables can be modified to meet geometric constraints and not exceed the thermal or structural design specifications. In general, the thermal response analysis of ablative thermal protection systems has traditionally been performed using a one-dimensional finite difference calculation. The structural analyses are generally one, two, or three-dimensional finite element calculations. In this dissertation, the governing differential equations for ablative thermal response are solved in three-dimensions using the finite element method. Darcy' Law is used to model the flow of pyrolysis gas through the ablative material. The three-dimensional governing differential equations for Darcy flow are solved using the finite element method as well. Additionally, the equations for linear elasticity are solved by the finite element method for the thermal stress using temperatures directly from the thermal response calculations. This dissertation also links the analysis of thermal protection systems to their design. The link to design comes from understanding the variation in the thermostructural response over the range of the design variables. Material property sensitivities are performed and an optimum design is determined based on a deterministic analysis minimizing the design specification of bondline temperature subject to appropriate constraints. A Monte Carlo simulation is performed on the optimum design to determine the probability of exceeding the design specifications. The design methodology is demonstrated on the Orion Crew Exploration Vehicle's compression pad design.Ph.D.Committee Chair: Dr. Robert D. Braun; Committee Member: Dr. David M. Schuster; Committee Member: Dr. Stephen M. Ruffin; Committee Member: Dr. Vitali Volovoi; Committee Member: Mr. Bernie Lau

Probabilistic Thermal Analysis During Mars Reconnaissance Orbiter Aerobraking

A method for performing a probabilistic thermal analysis during aerobraking has been developed. The analysis is performed on the Mars Reconnaissance Orbiter solar array during aerobraking. The methodology makes use of a response surface model derived from a more complex finite element thermal model of the solar array. The response surface is a quadratic equation which calculates the peak temperature for a given orbit drag pass at a specific location on the solar panel. Five different response surface equations are used, one of which predicts the overall maximum solar panel temperature, and the remaining four predict the temperatures of the solar panel thermal sensors. The variables used to define the response surface can be characterized as either environmental, material property, or modeling variables. Response surface variables are statistically varied in a Monte Carlo simulation. The Monte Carlo simulation produces mean temperatures and 3 sigma bounds as well as the probability of exceeding the designated flight allowable temperature for a given orbit. Response surface temperature predictions are compared with the Mars Reconnaissance Orbiter flight temperature data