Effects of elevated temperature on the viscoplastic modeling of graphite/polymeric composites

To support the development of new materials for the design of next generation supersonic transports, a research program is underway at NASA to assess the long term durability of advanced polymer matrix composites (PMC's). One of main objectives of the program was to explore the effects of elevated temperature (23 to 200 C) on the constitutive model's material parameters. To achieve this goal, test data on the observed nonlinear, stress-strain behavior of IM7/5260 and IM7/8320 composites under tension and compression loading were collected and correlated against temperature. These tests, conducted under isothermal conditions using variable strain rates, included such phenomena as stress relaxation and short term creep. The second major goal was the verification of the model by comparison of analytical predictions and test results for off axis and angle ply laminates. Correlation between test and predicted behavior was performed for specimens of both material systems over a range of temperatures. Results indicated that the model provided reasonable predictions of material behavior in load or strain controlled tests. Periods of loading, unloading, stress relaxation, and creep were accounted for

Rate dependent stress-strain behavior of advanced polymer matrix composites

The formulation of an elastic/viscoplastic constitutive model which was used to predict the measured behavior of graphite/thermoplastic and graphite/bismaleimide composite materials at elevated temperature is described. The model incorporates the concepts of overstress and effective strain/strain to provide a simple formulation which was able to account for material behavior under monotonic tension or compression loads over a temperature range of 23 to 200 C. Observed behavior such as stress relaxation and steady state creep, in off-axis tension and compression tests, were predicted by the model. Material constants required by the model were extracted from simple off-axis test data

Rate dependent constitutive models for fiber reinforced polymer composites

A literature survey was conducted to assess the state-of-the-art in rate dependent constitutive models for continuous fiber reinforced polymer matrix composite (PMC) materials. Several recent models which include formulations for describing plasticity, viscoelasticity, viscoplasticity, and rate-dependent phenomenon such as creep and stress relaxation are outlined and compared. When appropriate, these comparisons include brief descriptions of the mathematical formulations, the test procedures required for generating material constants, and details of available data comparing test results to analytical predictions

Matrix dominated stress/strain behavior in polymeric composites: Effects of hold time, nonlinearity and rate dependency

In order to understand matrix dominated behavior in laminated polymer matrix composites, an elastic/viscoplastic constitutive model was developed and used to predict stress strain behavior of off-axis and angle-ply symmetric laminates under in-plane, tensile axial loading. The model was validated for short duration tests at elevated temperatures. Short term stress relaxation and short term creep, strain rate sensitivity, and material nonlinearity were accounted for. The testing times were extended for longer durations, and periods of creep and stress relaxation were used to investigate the ability of the model to account for long term behavior. The model generally underestimated the total change in strain and stress for both long term creep and long term relaxation respectively

Apparatus for Elevated Temperature Compression or Tension Testing of Specimens

In order to support materials selection for the next generation supersonic civilian passenger transport aircraft, a testing apparatus was developed to evaluate certain materials under conditions of high load and elevated temperature. In order to elevate the temperature of the material during standard tension and compression testing the test specimen is surrounded by a pair of supports which include internal heating means. These supports also prevent buckling of the specimen during compression testing

Comparison of Some Exact and Perturbative Results for a Supersymmetric SU(NcN_c) Gauge Theory

We consider vectorial, asymptotically free ${\cal N}=1$ supersymmetric SU($N_c$) gauge theories with $N_f$ copies of massless chiral super fields in various representations and study how perturbative predictions for the lower boundary of the infrared conformal phase, as a function of $N_f$, compare with exact results. We make use of two-loop and three-loop calculations of the beta function and anomalous dimension of the quadratic chiral super field operator product for this purpose. The specific chiral superfield contents that we consider are $N_f$ copies of (i) $F+\bar F$, (ii) $Adj$, (iii) $S_2+\bar S_2$, and (iv) $A_2 + \bar A_2$, where $F$, $Adj$, $S_2$, and $A_2$ denote, respectively, the fundamental, adjoint, and symmetric and antisymmetric rank-2 tensor representations. We find that perturbative results slightly overestimate the value of $N_{f,cr}$ relative to the respective exact results for these representations, i.e., slightly underestimate the interval in $N_f$ for which the theory has infrared conformal behavior. Our results provide a measure of how closely perturbative calculations reproduce exact results for these theories.Comment: 16 pages, 3 figure

Time-Dependent Behavior of a Graphite/Thermoplastic Composite and the Effects of Stress and Physical Aging

Experimental studies were performed to determine the effects of stress and physical aging on the matrix dominated time dependent properties of IM7/8320 composite. Isothermal tensile creep/aging test techniques developed for polymers were adapted for testing of the composite material. Time dependent transverse and shear compliance's for an orthotropic plate were found from short term creep compliance measurements at constant, sub-T(8) temperatures. These compliance terms were shown to be affected by physical aging. Aging time shift factors and shift rates were found to be a function of temperature and applied stress

Modeling of Interfacial Modification Effects on Thermal Conductivity of Carbon Nanotube Composites

The effect of functionalization of carbon nanotubes on the thermal conductivity of nanocomposites has been studied using a multi-scale modeling approach. These results predict that grafting linear hydrocarbon chains to the surface of a single wall carbon nanotube with covalent chemical bonds should result in a significant increase in the thermal conductivity of these nanocomposites. This is due to the decrease in the interfacial thermal (Kapitza) resistance between the single wall carbon nanotube and the surrounding polymer matrix upon chemical functionalization. The nanocomposites studied here consist of single wall carbon nanotubes in a bulk poly(ethylene vinyl acetate) matrix. The nanotubes are functionalized by end-grafting linear hydrocarbon chains of varying length to the surface of the nanotube. The effect which this functionalization has on the interfacial thermal resistance is studied by molecular dynamics simulation. Interfacial thermal resistance values are calculated for a range of chemical grafting densities and with several chain lengths. These results are subsequently used in an analytical model to predict the resulting effect on the bulk thermal conductivity of the nanocomposite

Modeling and Testing of the Viscoelastic Properties of a Graphite Nanoplatelet/Epoxy Composite

In order to facilitate the interpretation of experimental data, a micromechanical modeling procedure is developed to predict the viscoelastic properties of a graphite nanoplatelet/epoxy composite as a function of volume fraction and nanoplatelet diameter. The predicted storage and loss moduli for the composite are compared to measured values from the same material using three test methods; Dynamical Mechanical Analysis, nanoindentation, and quasi-static tensile tests. In most cases, the model and experiments indicate that for increasing volume fractions of nanoplatelets, both the storage and loss moduli increase. Also, the results indicate that for nanoplatelet sizes above 15 microns, nanoindentation is capable of measuring properties of individual constituents of a composite system. Comparison of the predicted values to the measured data helps illustrate the relative similarities and differences between the bulk and local measurement techniques

Nonlinear Visco-Elastic Response of Composites via Micro-Mechanical Models

Micro-mechanical models for a study of nonlinear visco-elastic response of composite laminae are developed and their performance compared. A single integral constitutive law proposed by Schapery and subsequently generalized to multi-axial states of stress is utilized in the study for the matrix material. This is used in conjunction with a computationally facile scheme in which hereditary strains are computed using a recursive relation suggested by Henriksen. Composite response is studied using two competing micro-models, viz. a simplified Square Cell Model (SSCM) and a Finite Element based self-consistent Cylindrical Model (FECM). The algorithm is developed assuming that the material response computations are carried out in a module attached to a general purpose finite element program used for composite structural analysis. It is shown that the SSCM as used in investigations of material nonlinearity can involve significant errors in the prediction of transverse Young's modulus and shear modulus. The errors in the elastic strains thus predicted are of the same order of magnitude as the creep strains accruing due to visco-elasticity. The FECM on the other hand does appear to perform better both in the prediction of elastic constants and the study of creep response