Modeling the Non-linear Viscoelastic Response of High Temperature Polyimides

A constitutive model is developed to predict the viscoelastic response of polyimide resins that are used in high temperature applications. This model is based on a thermodynamic framework that uses the notion that the `natural configuration' of a body evolves as the body undergoes a process and the evolution is determined by maximizing the rate of entropy production in general and the rate of dissipation within purely mechanical considerations. We constitutively prescribe forms for the specific Helmholtz potential and the rate of dissipation (which is the product of density, temperature and the rate of entropy production), and the model is derived by maximizing the rate of dissipation with the constraint of incompressibility, and the reduced energy dissipation equation is also regarded as a constraint in that it is required to be met in every process that the body undergoes. The efficacy of the model is ascertained by comparing the predictions of the model with the experimental data for PMR-15 and HFPE-II-52 polyimide resins.Comment: 16 pages, 4 figures, submitted to Mechanics of Material

Two Simple Approximate Methods of Laplace Transform Inversion for Viscoelastic Stress Analysis

Two approximate methods of Laplace transform inversion are given which are simple to use and are particularly applicable to stress analysis problems in quasi-static linear viscoelasticity. Once an associated elastic solution is known numerically or analytically, the time-dependent viscoelastic response can be easily calculated using realistic material properties, regardless of how complex the property dependence of the elastic solution may be. The new feature of these methods is that it is necessary to know only 1) an elastic solution numerically for certain ranges of elastic constants and 2) numerical values of the operational moduli or compliances for real, positive values of the transform parameter. One method utilizes a mathematical property of the Laplace transform, while the other is based on some results obtained from Irreversible Thermodynamics and variational principles. Because of this, they are quite general and can be used with anisotropic and inhomogeneous materials. Two numerical examples are given: As the first one, we calculate the time-dependent strain in a long, internally. pressurized cylinder with an elastic case. The second example consists of inverting a transform which was derived by Muki and Sternberg in the thermo-viscoelastic analysis of a slab and a sphere(1). Both methods were found to provide results which are within the usual engineering requirements of accuracy. Application of the approximate methods to problems in dynamic viscoelasticity is discussed briefly. Supplementing the stress analysis, two techniques for calculating operational moduli and compliances from experimental stress-strain data are discussed and applied. Both can be used with creep, relaxation, and steady-state oscillation data. The most direct one consists of numerically integrating experimental data, while the other is a model-fitting scheme. With this latter method finite-element spring and dashpot models are readily found which fit the entire response.curves. In using these methods to calculate the operational functions employed in the stress analysis examples, we found that model-fitting was the fastest of the two, yet was very accurate

Fundamental Studies Relating to Systems Analysis of Solid Propellants

In this report the groundwork is laid for the proposed work scope which stressed the need for a greater understanding of the solid mechanics of grains. Particular emphasis will be directed toward the multi-axial behavior of thick walled configurations. The work falls naturally into three areas; (1) analysis procedures, (2) material properties, and (3) failure criteria. As a necessary preliminary to treating specific designs, certain material of general applicability must be developed, collected, and summarized. The following sections therefore deal with a general description of viscoelastic analysis and material representation, discussed by contrast with more conventional engineering analysis. By this means a background is established for the collection of elastic design formulas which are included in the second section of the report

A dynamical law for slow crack growth in polycarbonate films

We study experimentally the slow growth of a single crack in polycarbonate films submitted to uniaxial and constant imposed stress. For this visco-plastic material, we uncover a dynamical law that describes the dependence of the instantaneous crack velocity with experimental parameters. The law involves a Dugdale-Barenblatt static description of crack tip plastic zones associated to an Eyring's law and an empirical dependence with the crack length that may come from a residual elastic field

Fundamental Studies Relating to Systems Analysis of Solid Propellants

The earlier progress reports presented some essentials of model representation and a summary of some elastic solutions as preliminary material for viscoelastic analyses of solid propellants under various loading conditions. The present report is a continuation of the above with a brief section on Thermal Distributions, a section called Engineering Analysis, and one on Failure Criteria. The thermal distributions, obtained from heat transfer theory, are required for the thermoelastic formulations of section II. The Engineering Analysis section includes several varied examples to assist in understanding the analysis techniques presented in the other sections. The final section relates to mechanical failure of propellants and presents some preliminary thoughts as to how the study of this important problem area will be conducted

Compressive Strength and Failure Time Based on Local Buckling in Viscoelastic

The axial compressive strength and failure time of unidirectional, viscoelastic composites are investigated. Effects of nonlinear shear behavior and fiber misalignment are emphasized because they are important strength-limiting factors in those strongly anisotropic composites which fail by local buckling in the shear mode of deformation. We first describe the basic buckling model and then, neglecting hereditary effects, predict the compressive strengths of an untoughened and a rubber-toughened carbon/epoxy composite. Next, using a nonlinear viscoelastic constitutive equation for shear behavior, failure time for constant load and compressive strength for increasing load history are predicted by a numerical method. Additionally, approximate analytical formulas are developed which enable one to easily estimate buckling response as a function of initial fiber misalignment angle as well as loading and material parameters

A Simple Collocation Method for Fitting Viscoelastic Models to Experimental Data

An easily applied collocation method is discussed for fitting the response of finite-element viscoelastic models to experimental stress-strain curves. It can be used with creep, relaxation, and steady-state oscillation data. The method is illustrated by means of two examples. As the first one, a model is obtained utilizing the dynamic shear compliance of polyisobutylene. In the second example we calculate a model from the tensile relaxation modulus of polymethyl methacrylate. With each case the model's response agreed with the experimental data within graphical accuracy over the entire frequency (or time) scale

Cracking in asphalt materials

This chapter provides a comprehensive review of both laboratory characterization and modelling of bulk material fracture in asphalt mixtures. For the purpose of organization, this chapter is divided into a section on laboratory tests and a section on models. The laboratory characterization section is further subdivided on the basis of predominant loading conditions (monotonic vs. cyclic). The section on constitutive models is subdivided into two sections, the first one containing fracture mechanics based models for crack initiation and propagation that do not include material degradation due to cyclic loading conditions. The second section discusses phenomenological models that have been developed for crack growth through the use of dissipated energy and damage accumulation concepts. These latter models have the capability to simulate degradation of material capacity upon exceeding a threshold number of loading cycles.Peer ReviewedPostprint (author's final draft

Fracture toughness of acrylic resins: Viscoelastic effects and deformation mechanisms

The time dependence of fracture toughness of two different acrylic resins, one plain and one toughened, intended to be used as continuous fiber composite matrices was studied. By performing fracture tests following the fracture mechanics approach, the energy release rate, GIc, was determined at different temperatures and displacement rates and by applying the time-temperature superposition it was possible to obtain GIc as a function of crack speed, math formula, over a wide range of speeds. The trends obtained for the two resins were different. For the plain resin it could be well described by J. G. Williams' viscoelastic fracture theory while for the toughened resin, the trend obtained was attributed to a change in the damage mechanism occurring at the crack tip during fracture. From measurements of the process zone size it was deduced that the damage mechanism at the crack tip for the plain resin was the same irrespective of time and temperature, for the toughened resin instead, different mechanisms seem to take place. This hypothesis was supported by results of volume strain measurements in tensile tests at different temperature and strain rates