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

Three-Dimensional Finite Element Ablative Thermal Response and Thermostructural Design of Thermal Protection Systems

A finite element ablation and thermal response program is presented for simulation of three-dimensional transient thermostructural analysis. The three-dimensional governing differential equations and finite element formulation are summarized. A novel probabilistic design methodology for thermal protection systems is presented. The design methodology is an eight step process beginning with a parameter sensitivity study and is followed by a deterministic analysis whereby an optimum design can determined. The design process concludes with a Monte Carlo simulation where the probabilities of exceeding design specifications are estimated. The design methodology is demonstrated by applying the methodology to the carbon phenolic compression pads of the Crew Exploration Vehicle. The maximum allowed values of bondline temperature and tensile stress are used as the design specifications in this study

Ablative Thermal Response Analysis Using the Finite Element Method

A review of the classic techniques used to solve ablative thermal response problems is presented. The advantages and disadvantages of both the finite element and finite difference methods are described. As a first step in developing a three dimensional finite element based ablative thermal response capability, a one dimensional computer tool has been developed. The finite element method is used to discretize the governing differential equations and Galerkin's method of weighted residuals is used to derive the element equations. A code to code comparison between the current 1-D tool and the 1-D Fully Implicit Ablation and Thermal Response Program (FIAT) has been performed

Two-Dimensional Finite Element Ablative Thermal Response Analysis of an Arcjet Stagnation Test

The finite element ablation and thermal response (FEAtR, hence forth called FEAR) design and analysis program simulates the one, two, or three-dimensional ablation, internal heat conduction, thermal decomposition, and pyrolysis gas flow of thermal protection system materials. As part of a code validation study, two-dimensional axisymmetric results from FEAR are compared to thermal response data obtained from an arc-jet stagnation test in this paper. The results from FEAR are also compared to the two-dimensional axisymmetric computations from the two-dimensional implicit thermal response and ablation program under the same arcjet conditions. The ablating material being used in this arcjet test is phenolic impregnated carbon ablator with an LI-2200 insulator as backup material. The test is performed at the NASA, Ames Research Center Interaction Heating Facility. Spatially distributed computational fluid dynamics solutions for the flow field around the test article are used for the surface boundary conditions

Stochastics theory of log-periodic patterns

We introduce an analytical model based on birth-death clustering processes to help understanding the empirical log-periodic corrections to power-law scaling and the finite-time singularity as reported in several domains including rupture, earthquakes, world population and financial systems. In our stochastics theory log-periodicities are a consequence of transient clusters induced by an entropy-like term that may reflect the amount of cooperative information carried by the state of a large system of different species. The clustering completion rates for the system are assumed to be given by a simple linear death process. The singularity at t_{o} is derived in terms of birth-death clustering coefficients.Comment: LaTeX, 1 ps figure - To appear J. Phys. A: Math & Ge